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Note: Ignatius' information available here; verses number according to J.B.Lightfoot translation

1. Introduction:

The Ignatius' epistles are actually existing in several collections, but the seven ones of the middle recension are the only one widely accepted as authentic.
The seven epistles of the middle recension are:
1) 'to the Ephesians' (Ephes.)
2) 'to the Magnesians' (Magn.)
3) 'to the Trallians' (Trall.)
4) 'to the Romans' (Rom.)
5) 'to the Philadelphians' (Philad.)
6) 'to the Smyrnaeans' (Smyrn.)
7) 'to Polycarp' (Polyc.)
Five of these letters are seemingly addressed to Christians in cities of the Roman province of Asia; the last one to the bishop of Smyrna.
Several other recensions are also known, including the longer one with the initial seven letters greatly "updated" & embellished, plus an account ('Martyrium Ignatii') of Ignatius' condemnation by Trajan himself in Antioch (Syria), trip to Rome & martyrdom there (with a post-mortem reappearance!). But all of them are considered spurious and written not before the 4th/5th century. More so because Eusebius, writing around 315, is totally unaware of those. However he named Ignatius & the seven letters, gave two quotes and some indication on their content ('The History of the Church' (HC), 3, 36).
From the seven aforementioned letters --the commentaries of the fathers, up to Eusebius included, do not divulge much more-- very few historical items appear about Ignatius:
He is a Christian from Syria:
"the church which is in Syria,
[Antioch is specified only in the last three letters]
` whence I am led a prisoner to Rome -- I who am the very last of the faithful there;" (Ephes.21:1)
"the church which is in Syria, whereof I am not worthy to be called a member" (Magn.14:1)
and also its bishop, which is specified only once, in the fourth letter, and in passing:
"... for that God has vouchsafed that the bishop from Syria should be found in the West, having summoned him from the East" (Rom.2:2b)
Because of his faith, he is condemned (no detail available) to be executed as an offering to wild beasts. No indication is given about the year.
With his guards, he travels as a prisoner to Rome in the summer (Rom.10:3). He seems to go through Philadelphia, Asia minor (about eighty miles inland and east of Smyrna):
Philad.7:1b "... I cried out, when I was among you; I spoke with a loud voice, with God's own voice, Give you heed to the bishop and the presbytery and deacons."
He reaches Smyrna on the coast and stays here for a while. That allows him to receive bishops (and their entourage) from nearby cities (Ephesus, Magnesia & Tralles) and also write an epistle for each of these communities, plus one to the Romans. Later, he goes northward to Troas and, before sailing to Neapolis/Philippi (Polyc.8:1), he writes two epistles to Christian communities he visited before, Philadelphia & Smyrna (without naming their respective bishop!), plus one to Polycarp (the bishop of Smyrna).
Three of the main recurring themes in the epistles are:
- for a "heeded" bishop ruling over the presbyters/deacons and the faithful in each city, uniting all the (mainstream) Christians into a well-disciplined church (exception: 'to the Romans')
- for "Catholic" beliefs (as drawn from the gospels & Paul's epistles), with significant variations between letters
- against Gnosticism/Docetism ('to the Trallians, Smyrnaeans') and Judaism ('to the Magnesians, Philadelphians')

Eusebius confirmed Ignatius as the bishop of Antioch (HC, 3, 36), the alleged successor of Evodius "the first bishop" (HC, 3, 22).
Eusebius added he had (unspecified) evidence Ignatius "became food for wild animals" in Rome (in the letters, this is the condemnation, but obviously it was not carried out yet). Furthermore, by locating Ignatius' passage at the end of chapter 3, he suggested the martyrdom took place during Trajan's reign (98-117) (HC, 3, 36).
Later, more letters and details will appear (some three or more centuries after 110!), such as Ignatius' epistles to Mary (Jesus' mother) & to John the apostle, his long-lasting friendship with Polycarp and being the little child in Matthew18:2!

The seven letters are considered quasi-canonical by the Catholic Church (& some other ones) and the historical justification for many of its doctrines. One of the reasons would be Ignatius' alleged acquaintance with Jesus' disciples, as first "revealed" centuries later by bishops John Chrysostom (347-407) & Theodoret (393-457).
From the "Catholic Encyclopedia, St. Ignatius of Antioch":
"St. John Chrysostom lays special emphasis on the honor conferred upon the martyr in receiving his episcopal consecration at the hands of the Apostles themselves ("Hom. in St. Ig.", IV. 587). Natalis Alexander quotes Theodoret to the same effect (III, xii, art. xvi, p. 53)."
"Theodoret ("Dial. Immutab.", I, iv, 33a, Paris, 1642) is the authority for the statement that St. Peter appointed Ignatius to the See of Antioch"
And from the 'Martyrium Ignatii', ch.1:
"Ignatius, the disciple of John the apostle, a man in all respects of an apostolic character"
All of these seem to be embellishments on a claim Eusebius wrote earlier:
HC, 3, 37-38 "... But since it is impossible for us to enumerate the names of all that became shepherds or evangelists in the churches throughout the world in the age immediately succeeding the apostles, we have recorded, as was fitting, the names of those only who have transmitted the apostolic doctrine to us in writings still extant. Thus Ignatius has done in the [seven] epistles which we have mentioned ..."

Also from the "Catholic Encyclopedia, St. Ignatius of Antioch":
"Cardinal Newman did not exaggerate the matter when he said ("The Theology of the Seven Epistles of St. Ignatius", in "Historical Sketches", I, London, 1890) that "the whole system of Catholic doctrine may be discovered, at least in outline, not to say in parts filled up, in the course of his seven epistles". Among the many Catholic doctrines to be found in the letters are the following: the Church was Divinely established as a visible society, the salvation of souls is its end, and those who separate themselves from it cut themselves off from God (Philad., c. iii); the hierarchy of the Church was instituted by Christ (lntrod. to Philad.; Ephes., c. vi); the threefold character of the hierarchy (Magn., c. vi); the order of the episcopacy superior by Divine authority to that of the priesthood (Magn., c. vi, c. xiii; Smyrn., c. viii;. Trall., .c. iii); the unity of the Church (Trall., c. vi;Philad., c. iii; Magn., c. xiii); the holiness of the Church (Smyrn., Ephes., Magn., Trall., and Rom.); the catholicity of the Church (Smyrn., c. viii); the infallibility of the Church (Philad., c. iii; Ephes., cc. xvi, xvii); the doctrine of the Eucharist (Smyrn., c. viii), which word we find for the first time applied to the Blessed Sacrament, just as in Smyrn., viii, we meet for the first time the phrase "Catholic Church", used to designate all Christians; the Incarnation (Ephes., c. xviii); the supernatural virtue of virginity, already much esteemed and made the subject of a vow (Polyc., c. v); the religious character of matrimony (Polyc., c. v); the value of united prayer (Ephes., c. xiii); the primacy of the See of Rome (Rom., introd.)."
Please note some of the claims made here are not obviously backed up by the mentioned chapters, but can be extrapolated (or interpreted) from them as such.

2. The external evidence:

Despite the importance of Ignatius' letters and martyrdom, the external evidence is rather weak.

2.1 Polycarp:
The first one comes from the 'Polycarp to the Philippians' letter. It is generally not contested as being written by Polycarp (died around 155-167), because Irenaeus (wrote circa.180) knew him personally and provided details of his activities ('Against Heresies'(AH), III, 3, 4; letter to Florinus; letter to Victor), including the writing of the aforementioned epistle.
In the epistle, the name 'Ignatius' appears in two passages (9:2-3 & 13:1-2).

The second one is the most important. It reads:
13:1 "You wrote to me, both you yourselves and Ignatius [Polyc.7:2;8:2], asking that if any one should go to Syria he might carry thither the letters from you. And this I will do, if I get a fit opportunity, either I myself, or he whom I shall send to be ambassador on your behalf also.
13:2 The letters of Ignatius which were sent to us by him, and others as many as we had by us, we send unto you, according as you gave charge [you asked]; the which are subjoined to this letter; from which you will be able to gain great advantage. For they comprise faith and endurance and every kind of edification, which pertains unto our Lord. Moreover concerning Ignatius himself and those that were with him, if you have any sure tidings, certify us."
The last sentence of the quote would date the letter to no more than a few weeks after Ignatius went through the area. But then we have two problems:
A) The letter is not about Ignatius, but about answering concerns from the Philippians, at their request:
3:1 "These things, brethren, I write unto you concerning righteousness, not because I laid this charge upon myself, but because you invited me."
at a time when one of them, an ex-presbyter, had abused his office (11:1-4).
Therefore, it would be too much of a coincidence the letter was written when Ignatius happened to be on his way to Rome.
B) Another problem comes from this verse:
7:1 "For every one who shall not confess that Jesus Christ is come in the flesh, is antichrist: and whosoever shall not confess the testimony of the Cross, is of the devil; and whosoever shall pervert the oracles of the Lord to his own lusts and say that there is neither resurrection nor judgment, that man is the firstborn of Satan."
This seems to be directed against Gnostics, more so Basilides, whom, according to Eusebius, came during the rule of Hadrian (117-138). It is generally agreed those Gnostics (such as Basilides) started to have an impact on Christianity not earlier than 120-125.
Let's consider the following:
a) "not confess that Jesus Christ is come in the flesh"
Basilides thought that Jesus was incorporeal:
As reported by Irenaeus, about Basilides, AH, I, 24, 4 "For since he was an incorporeal power, and the Nous (mind) of the unborn father, he transfigured himself as he pleased, and thus ascended to him who had sent him, deriding them, inasmuch as he could not be laid hold of, and was invisible to all"
b) "not confess the testimony of the Cross"
Basilides did not believe Christ was crucified:
As reported by Irenaeus, about Basilides, AH, I, 24, 4 "[Basilides thought] He appeared, then, on earth as a man, to the nations of these powers, and wrought miracles. Wherefore he did not himself suffer death, but Simon, a certain man of Cyrene, being compelled, bore the cross in his stead, so that this latter being transfigured by him, that he might be thought to be Jesus, was crucified, through ignorance and error, while Jesus himself received the form of Simon, and, standing by, laughed at them."
c) "pervert the oracles of the Lord to his own lusts"
Basilides was accused of immoralities:
As reported by Irenaeus, about Basilides, AH, I, 24, 5 "he holds also the use of other things, and the practice of every kind of lust, a matter of perfect indifference."
d) "there is neither resurrection, nor judgment"
Basilides did not believe in bodily resurrection:
As reported by Irenaeus, about Basilides, AH, I, 24, 5 "Salvation belongs to the soul alone, for the body is by nature subject to corruption."
Basilides was from Alexandria and active around 120-140. His "teachings" were vehemently refuted then by the "Catholic" Church:
Eusebius (HC, 4, 7): "There has come down to us a most powerful refutation of Basilides by Agrippa Castor, one of the most renowned writers of that day, which shows the terrible imposture of the man."

It is obvious Polycarp's letter was not issued during Trajan's reign but decade(s) afterwards. Consequently, if the Ignatian letters were composed under Trajan, verses 13:1-2 have to be a later interpolation.

Now let's look at the other occurrence of 'Ignatius' in the same epistle:
9:1 "I exhort you all therefore to be obedient unto the word of righteousness and to practice all endurance, which also you saw with your own eyes in the blessed Ignatius and Zosimus and Rufus, yea and in others also who came from among yourselves, as well as in Paul himself and the rest of the Apostles;
9:2 being persuaded that all these ran not in vain but in faith and righteousness, and that they are in their due place in the presence of the Lord, with whom also they suffered. ..."
Comments:
a) At first look, it seems to deal with martyrs (as generally thought). But is it so?
It is only expressed those men "suffered" (when they preached) and NOT 'got executed'. And what the Philippians "saw with your own eyes" are obedience "unto the word of righteousness" and practice of "all endurance", not martyrdom. Furthermore, it has never been written "the rest of the Apostles" died as martyrs.
So, verses 9:1-2 are most likely about Christian preachers, who, after an exemplary life with righteousness, endurance, faith & associated sufferance, allegedly got their rewards in heaven (but not necessarily through martyrdom!).
b) "the blessed Ignatius" is suspicious. Why would Ignatius be qualified as "blessed" and not Paul (as in 3:2 "the blessed and glorious Paul" and in 11:3 "among whom the blessed Paul labored")?
If Polycarp did not want to differentiate here between Paul and the others (many not named), therefore not qualifying Paul as "blessed" (as in 11:2), why would he do so for Ignatius?

It is likely an interpolator, thinking the passage was about martyrs, added up "the blessed Ignatius and" to the others (and in front!): Ignatius' name had to be included in 9:1-2, more so because, allegedly, the blessed martyr went through Philippi!
After all, 13:1-2 is considered an interpolation by some scholars and another one, more minor, could have been made at verse 9:1.

Notes:
a) In 13:1-2, "Ignatius" (not "blessed" here) is still on his way to Rome. In 9:1-2, "blessed Ignatius" is already in heaven! This is a sure sign that one (at least) of the two passages was interpolated.
b) "For I wrote letters when the brethren requested me to write. And these letters the apostles of the devil have filled with tares, taking away some things and adding others, ..." Dionysius, bishop of Corinth (165-175), fragments from a letter to the Roman church

2.2 Irenaeus:
'Against Heresies'(AH), V, 28, 4, written circa.180 "As a certain man of ours said, when he was condemned to the wild beasts because of his testimony with respect to God: "I am the wheat of Christ, and am ground by the teeth of the wild beasts, that I may be found the pure bread of God. [Rom.4:1b]""
This is the only piece in Irenaeus' works dealing with Ignatius. But then, why did Irenaeus NOT specify Ignatius as the author of the quote? "Ignatius" appears in the introduction of 'to the Romans' and cannot be missed.
Furthermore Irenaeus wrote three long passages mentioning Polycarp (AH, III, 3, 4; letter to Florinus; letter to Victor), including "Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ", but never brought up Ignatius in them.
Why not call the name of a celebrated martyr, a great friend of Polycarp (as claimed later) and bishop (like Irenaeus)?
And Irenaeus knew about the letter Polycarp sent to the Philippians (the main external evidence for Ignatius, as believed by most scholars):
"There is also a most powerful epistle written by Polycarp to the Philippians ..." (AH, III, 3, 4)
Considering the very "Catholic" letters by a bishop written very early would be a formidable weapon against heresies, it seems Irenaeus avoided 'Ignatius' & his alleged letters because of the controversial nature of those.

2.3 Origen:
"Origen twice refers to him, first in the preface to his Comm. on the Song of Solomon, where he quotes a passage from the Epistle of Ignatius to the Romans, and again in his sixth homily on St. Luke, where he quotes from the Epistle to the Ephesians, both times naming the author."
Introductory Note to the Epistle of Ignatius to the Ephesians, Roberts-Donalson
Origen wrote circa.220-250

2.4 Eusebius:
Eusebius, writing around 315, reported about the seven letters and Ignatius, in relative low-key terms (HC, 3, 36). He also quoted the passages from Polycarp & Irenaeus relative to Ignatius. However, he introduced Ignatius as follows:
"... one who to this day is universally remembered - Ignatius ..."
without giving any more details than the ones already available from the seven letters (except for the fulfillment of Ignatius' martyrdom, and during Trajan's reign).
According to the aforementioned quote, it seems Eusebius was intent to "prove" Ignatius in his 'History of the Church'. More as follows:
a) The only quotes that Eusebius gave from Polycarp's letter is about the two passages mentioning Ignatius (HC, 3, 36).
b) Eusebius introduced the brief & incomplete Irenaeus' testimony about Ignatius as such:
"His martyrdom was well known to Irenaeus, who draw on his epistles: [as already quoted, with no naming by Irenaeus of Ignatius & the (only one) letter!] ..." (HC, 3, 36)

Let's note Eusebius reproduced long detailed stories about the martyrdom of second century Christians (HC, 4, 15; HC, 4, 17; HC, 5, 1), but the one about Ignatius is lacking.

The external evidence about Ignatius, up to two centuries after his alleged time, is very small. That is unexpected, considering the epistles would be a boon for early (Catholic) Christianity and show Ignatius as a superlative martyr & bishop. The reason may be that, up to then, the authenticity of Ignatius' letters was highly suspect.

3. The incongruities in Ignatius' story:

The circumstances leading to the writing of the letters are unrealistic.

3.1 Ignatius is condemned to death in Antioch and sent to Rome for execution:
Why would someone condemned "for the sake of the common Name and hope" (Ephes.1:2) be sent away to Rome?
According to Ac25:10-12 and the famous Pliny's letter about Christians, Roman citizens could go to Rome for judgment, but NOT for execution after being condemned somewhere else. And answering the aforementioned letter, emperor Trajan did not reprimand Pliny for not sending to Rome the convicted Christians!
Ignatius' condemnation is about becoming food for the wild beasts. Would that mean having to go to Rome for that?
In the spurious 'Acts of Paul & Thecla', the heroine, Thecla, is thrown to the beasts in the arena of Antioch, the city of Ignatius. The author certainly thought this kind of things could happen there!
Also, in a more realistic account, as related in Eusebius' HC, 5, 1, Christians in Gallic cities were executed there by being offered to wild beasts, towards the end of the second century.

Simply, Ignatius' condemnation in Syria and then his dispatch to Rome (at great expense for the Romans) do not make any sense. Furthermore, a public execution by torture was a strong deterrent for the ones who knew the condemned, but not for strangers in a remote city.

3.2 Ignatius, as a prisoner, is passing through Smyrna, on his way to Rome from Antioch:
The map below gives the location of the three cities plus the normal itineraries towards Rome, by sea (in blue) or land (in brown).
The gray line is the itinerary according to the 'Martyrium Ignatii'. The continuous brown line shows an overland route through Philadelphia (according to Philad.7:1 and conflicting with the Martyrium!).
Let's notice the sea crossing from Troas to Philippi (Neapolis), as for Paul in 'Acts' (16:11)!

Note: in the seven letters of the middle recension, only the section 'Philadelphia, Smyrna, Troas & Philippi (Neapolis)' is alluded to.

In the Roman empire, sailing was the preferred mode of transportation for goods, people and prisoners. In all likelihood, a prisoner then would be sent by ship, as from Antioch to Rome, two cities close to the sea.
Paul and other prisoners went by boat from Judea to Italy (Ac27-28). And for Jews taken from Jerusalem in 70C.E., Titus ordered "the captives should be kept there [in Cesarea, and at great expense!]; for the winter season hindered him then from sailing into Italy." (Josephus' Wars,VII,I,3)
Rather than travelling on land in winter, waiting for spring & sailing season was preferable. Furthermore, a small company of soldiers going through rugged terrain would be an easy ambush for rebels.
The two indicated sea routes, one direct through the open sea, the other, more sheltered, through the Corinthian isthmus, would be the ones used between northern Syria and Italy. Smyrna, completely off-route, and at the end of a forty miles long bay opening to the NW, is therefore totally unrealistic as a place where Ignatius & guards would have stopped on their way to Rome. Let's note the 'Martyrium Ignatii' has them going from Seleucia (the harbour of Antioch) to Smyrna by sea, without explaining why they would land into the later city.
And in the very small probability (more so in summer --Rom.10:3) an overland route was used, then the most logical way would be by crossing the Bosphorus, as indicated on the map. An important Roman military road was linking Antioch with Byzantium (today Istanbul).

3.3 Ignatius, as a prisoner, is the host of Christian clerics:
Ignatius, as a condemned man because of his faith, is allowed to talk with small groups of prominent Christians (or the whole community, as for Philadelphia!) and even issue letters propagating his reprimanded beliefs!
There is a lot of similarities with Paul, as in Ac27:3;28:14,17-31, 'Philippians', 'Colossians', 'Philemon' & '1Timothy', but here Paul is not judged & condemned yet and has Roman citizenship (according to 'Acts').
And the bishops, with some of their presbyters & deacons, would be in great danger when requesting to see Ignatius. But in the Ignatian letters, there is nothing about those visitors putting themselves at risk! And one of them, Burrhus, a deacon from Ephesus, accompanies Ignatius from Smyrna to Troas (Ephes.2:1; Philad.11:2; Smyrn12:1), as his personal servant/scribe!

4. Were the seven epistles written by the same person?

It is undeniable:
a) There are many similarities in the wording of the seven epistles.
b) Each epistle was written with the knowledge of all (or most of) the earlier ones.
However, there are also many contradictions & oddities between epistles, raising doubts about their writing by a same author (& within a few weeks!). Let's examine the main ones:

4.1 About bishops:
Six of the seven letters emphasize the necessity & importance of the bishop (with his presbyters/deacons), as the head & ruler for each city-based Christian community:

'To the Ephesians':
"... submitting yourselves to your bishop and presbytery, you may be sanctified in all things." (2:2)
"... Plainly therefore we ought to regard the bishop as the Lord Himself." (6:1)
Also 4:1,5:2-3,20:2
'To the Magnesians':
"... I advise you, be you zealous to do all things in godly concord, the bishop presiding after the likeness of God and the presbyters after the likeness of the council of the Apostles, with the deacons also who are most dear to me ..." (6:1)
"Therefore as the Lord did nothing without the Father, either by Himself or by the Apostles, so neither do you anything without the bishop and the presbyters ..." (7:1)
Also 2:1,6:2,13:2
'To the Trallians':
"For when you are obedient to the bishop as to Jesus Christ ..." (2:1)
"you should do nothing without the bishop; but be you obedient also to the presbytery" (2:2)
"In like manner let all men respect the deacons as Jesus Christ, even as they should respect the bishop as being a type of the Father and the presbyters as the council of God and as the college of Apostles." (3:1)
Also 7:1-2,13:2
'To the Philadelphians':
"I spoke with a loud voice, with God's own voice, Give you heed to the bishop and the presbytery and deacons." (7:1)
"... Do nothing without the bishop. Do you all follow your bishop, as Jesus Christ followed the Father, and the presbytery as the Apostles; and to the deacons pay respect, as to God's commandment ..." (7:2)
Also 0:0,3:2,4:1,8:1
'To the Smyrnaeans':
"Do you all follow your bishop, as Jesus Christ followed the Father, and the presbytery as the Apostles; and to the deacons pay respect, as to God's commandment" (8:1)
"Wheresoever the bishop shall appear, there let the people be; even as where Jesus may be, there is the universal Church. It is not lawful apart from the bishop either to baptize or to hold a love-feast; but whatsoever he shall approve, this is well-pleasing also to God; that everything which you do may be sure and valid." (8:2)
"... It is good to recognize God and the bishop. He that honours the bishop is honoured of God ..." (9:1)
'To Polycarp':
"... If he boast, he is lost; and if it be known beyond the bishop, he is polluted. It becomes men and women too, when they marry, to unite themselves with the consent of the bishop, that the marriage may be after the Lord and not after concupiscence ..." (5:2)
"Give you heed to the bishop, that God also may give heed to you. I am devoted to those who are subject to the bishop, the presbyters, the deacons ..." (6:1)

Clearly, bishops had to be acknowledged in many ways. But what do we see in 'to the Romans'?
Contrary to the other letters, where the bishop of the community is referred to (and in excellent terms), the Roman bishop is ignored totally: there is no mention he exists.
In this epistle, where the support & prayers from the whole Christian community of Rome are requested, there is no mention of a local bishop! That clashes drastically with the treatment of bishops, either generally or specifically, in the other six letters. And there are no mentions of presbyters, presbytery & deacons (who certainly existed in Rome then), in the whole epistle!

Note: occurrences for 'presbyters' + 'presbytery' + 'deacons':
Ephes.=3, Magn.=8, Trall.=9, Rom.=0, Philad.=8, Smyrn.=3, Polyc.=2

Note: 'to the Romans' is also unique because, only here, Ignatius is declared a bishop ...

4.2 Who raised Jesus?
There are two letters which indicate who raises Jesus:

'To the Trallians':
"[Jesus] was truly crucified and died in the sight of those in heaven and those on earth and those under the earth; who moreover was truly raised from the dead, His Father having raised Him ..." (9:1b-2a)
'To the Smyrnaeans':
"For He [Jesus] suffered all these things for our sakes; and He suffered truly, as also He raised Himself truly ..." (2:1)
However, in the same letter we have:
"... They abstain from eucharist (thanksgiving) and prayer, because they allow not that the eucharist is the flesh of our Saviour Jesus Christ, which flesh suffered for our sins, and which the Father, of His goodness, raised up." (6:2)
The words shown in purple are most likely a later "corrective" interpolation because:
a) They seem a digression at the end of an already long sentence.
b) Jesus' flesh (instead of Jesus himself) being raised is very awkward.
c) It is conflicting with 2:1. 'Who raised Jesus' is an important theological matter and a same Christian writer could not have it both ways.

What is there to conclude?
It is highly probable 'to the Trallians' and 'to the Smyrnaeans' have different authors.

4.3 Was Jesus pre-existent?
Only one letter has Jesus as pre-existent. And in it, there are not one, but three references.

'to the Magnesians':
"... Jesus Christ, who was with the Father before the worlds and appeared at the end of time." (6:1)
"... Jesus Christ, who came forth from One Father ..." (7:2)
"... the divine prophets lived after Christ Jesus. For this cause also they were persecuted, being inspired by His grace to the end ... Jesus Christ His Son, who is His Word that proceeded from silence, who in all things was well-pleasing unto Him that sent Him." (8:2)

Note: in the same epistle, Jesus performed a feat never mentioned before:
"... He whom they [the prophets] rightly awaited, when He [Jesus] came, raised them from the dead." (9:2b)

Three other letters seem to deny the pre-existence:

'To the Ephesians':
"For our God, Jesus the Christ, was conceived in the womb by Mary according to a dispensation, of the seed of David but also of the Holy Ghost; and He was born ... And hidden from the prince of this world were the virginity of Mary ..." (18:2-19:1a)
'To the Trallians':
"... Jesus Christ, who was of the race of David, who was the Son of Mary, who was truly born ..." (9:1)
In this letter, there is no mention of the Holy Ghost (or God) involvement in the conception (and NO virgin & Son (of God) either).
'To the Smyrnaeans':
"... He is truly of the race of David according to the flesh, but Son of God by the Divine will and power, truly born of a virgin ..." (1:1)

It is unlikely the author of 'to the Magnesians' was the same as the one(s) of 'to the Ephesians', 'to the Trallians', 'to the Smyrnaeans' or any other letters: why mention three times the pre-existence of Christ in one letter, then ignore this important issue in all the other epistles?
And why is the 'virgin conception' inexistent in 'to the Trallians'?
Probably because the author was different of the one(s) of 'to the Ephesians' and 'to the Smyrnaeans'.

4.4 Syria and Antioch:
Each one of the first four letters (allegedly written from Smyrna) specifies Ignatius' church is in Syria (a large province with many cities!), without indicating which city:
"Pray for the church which is in Syria, whence I am led a prisoner to Rome ..." (Ephes.21:2)
"... remember also the church which is in Syria, whereof I am not worthy to be called a member ..." (Magn.14:1)
"... Remember in your prayers the church which is in Syria; whereof I am not worthy to be called a member ..." (Trall.13:1)
"... the bishop from Syria should be found in the West, having summoned him from the East ..." (Rom.2:2)
"Remember in your prayers the church which is in Syria, which has God for its shepherd in my stead ..." (Rom.9:1)
The question is begged, 'where in Syria?'. More so because it is unrealistic, in an age of very slow communication (for ideas and people), Ignatius would be the bishop of the whole of Syria; since a bishop, according to the other epistles, should be omnipotent & omnipresent within the Christian community of his city.

However, in each of the last three letters (allegedly written from Troas), at last, the city is indicated: it is Antioch!
"... it has been reported to me that the church which is in Antioch of Syria has peace ..." (Philad.10:1)
"Your prayer sped forth unto the church which is in Antioch of Syria; whence coming a prisoner ..." (Smyrn.11:1)
"Seeing that the church which is in Antioch of Syria has peace ..." (Polyc.7:1)

Could a same author ignore (or forget) the city in his first four letters, then name it in the last three?
Antioch was then the third largest city in the Roman empire (about 800,000 inhabitants), the first main Christian center and the starting point of Paul's apostolic career: nothing to be ashamed of!
The lack of mention of 'Antioch' in the first four letters points to a different authorship.

4.5 The envoy to Antioch:
The last two letters mention sending someone to Antioch, but for different purposes:

'To the Smyrnaeans':
"Therefore that your work may be perfected both on earth and in heaven, it is meet that your church should appoint, for the honour of God, an ambassador of God that he may go as far as Syria and congratulate them because they are at peace, and have recovered their proper stature, and their proper bulk has been restored to them." (11:2)
An appointee from the church of the Smyrnaeans (the one ruled by Polycarp!) should go to Antioch in order to felicitate the church there about their peace and recovery.
'To Polycarp':
"It becomes thee, most blessed Polycarp, to call together a godly council and to elect some one among you who is very dear to you and zealous also, who shall be fit to bear the name of God's courier -- to appoint him, I say, that he may go to Syria and glorify your zealous love unto the glory of God." (7:2)
Now the appointee is mainly someone very dear to the bishop of Smyrna, and whose goal is to glorify Polycarp among the Antiochenes.

The same elected/appointee from Smyrna has two different purposes, one per letter! The two epistles could not have been written by the same person. That becomes even more evident when the next point is considered ...

4.6 Ignatius and Polycarp:
In the later quote Ignatius is emphatically praising Polycarp, as also in:
"... Knowing the fervour of your sincerity ..." (Polyc.7:3)
"... you may be glorified by an ever memorable deed -- for this is worthy of thee." (Polyc.8:1)
And the last (7th) letter, 'to Polycarp', is the only one to be addressed to an individual, showing (allegedly) Ignatius has high regard for Polycarp.
But, as also quoted, the preceding letter, 'to the Smyrnaeans', totally ignores the local bishop (that is Polycarp himself) when choosing the envoy to Syria. More, the name 'Polycarp' does not appear in the (6th) epistle at all!
Certainly, the Smyrnaeans are reported to have a bishop, but only presented as a "standard" one, with no personal traits, except he is godly (but so is "Damas, your godly bishop" Magn.2:1):
"I salute your godly bishop and your venerable presbytery [and] my fellow-servants the deacons ..." (12:2)
That's in sharp contrast with the ones of Ephesus (Onesimus), Magnesia (Damas), Tralles (Polybius) and Philadelphia (unnamed), to whom personal characteristics are attributed.
And there is nothing in 'to the Smyrnaeans' to indicate Ignatius knew or met the bishop (who did not have to go far to see him!). Actually, the locals named in the epistle are not even said to be presbyters or deacons:
"I salute the household of Gavia, and I pray that she may be grounded in faith and love both of flesh and of spirit. I salute Alce, a name very dear to me, and Daphnus the incomparable, and Eutecnus, and all by name ..." (13:2)
'Polycarp' does not appear in 'to the Philadelphians'. And in the first four letters, all of them allegedly written from Smyrna, Polycarp is named in only two:
"I am devoted to you and to those whom for the honour of God you sent to Smyrna; whence also I write unto you with thanksgiving to the Lord, having love for Polycarp as I have for you also." (Ephes.21:1)
"The Ephesians from Smyrna salute you, from whence also I write to you. They are here with me for the glory of God, as also are you; and they have comforted me in all things, together with Polycarp bishop of the Smyrnaeans ..." (Magn.15:1)
In view of the treatment of Polycarp in 'to the Smyrnaeans', we have the right to be suspicious about these two clauses with 'Polycarp' (in purple). More so considering:
a) Both appear at the end of their respective epistle, extend an already long sentence and seem to be a digression.
b) How could the same author introduce 'Polycarp' with so much dissimilarity?
- In the first one, it looks like name-dropping. Polycarp is casually named, he is loved, but also the Ephesians at large whom Ignatius never met!
- In the second one, Polycarp is "officially" described. Let's note it is very similar to "Polycarp who is bishop of the church of the Smyrnaeans" (Polyc.0:0) in the last epistle; and in the first six letters, nobody else is declared "bishop (of the church) of 'the inhabitants of a city' OR 'a city'.
And it is suggested Ignatius met Polycarp then, but this is never indicated in the first six letters, even rather denied in 'to the Smyrnaeans'. Only in the last one we have:
"it has been vouchsafed me to see thy blameless face [of Polycarp]" (Polyc.1:1)
which does not say anything about talks then, in contrast with the description of meetings with the other bishops.
c) 'To the Trallians', 'to the Romans' & 'to the Smyrnaeans' reproduce many items from the first two epistles, but NO 'Polycarp' shows in them.

In conclusion, it seems the first six epistles made no mention of 'Polycarp' (initially). The author of 'to Polycarp' could not have been the one of 'to the Smyrneans', and it is unlikely he was the one of any of the other epistles.

4.7 Jesus as "our God":
The epistle 'to the Ephesians' features three times Jesus Christ as "our God":
"... by the will of the Father and of Jesus Christ our God ..." (0:0)
"... He [the Lord] Himself may be in us as our God ..." (15:3)
"For our God, Jesus the Christ, was conceived in the womb by Mary ..." (18:2)
Only 'to the Romans' has several of those:
"... by faith and love towards Jesus Christ our God ..." (0:0)
"... abundant greeting in Jesus Christ our God ..." (0:0)
"... For our God Jesus Christ, being in the Father, is the more plainly visible ..." (3:3)
Besides that, the only other occurrence is in 'to Polycarp':
"I bid you farewell always in our God Jesus Christ ..." (8:3)
Why are there NO 'Jesus Christ as "our God" (a very important --and somewhat heretical-- christological claim) in 'to the Magnesians', 'to the Trallians' and 'to the Philadelphians', when it appears three times in the first (& fourth) epistle?
A common author would have reproduced this important claim, in one form or another, in most, if not all, of his other letters. Let's note also that in 'to the Trallians' and 'to the Philadelphians', Jesus is not declared as "the Son", only as "God the Father" being "his Father".
The former epistle depicts a very human origin for Christ (Trall.9:1, as already quoted) and the later sets him very distinct of God (the Father):
"... in the love of God the Father and the Lord Jesus Christ ..." (Philad.1:1)
"For as many as are of God and of Jesus Christ ..." (Philad.3:2)

4.8 'Gospel':
In all the seven epistles, the word 'gospel' appears in only two of those, six times in 'to the Philadelphians' and twice in 'to the Smyrnaeans'.
'To the Philadelphians':
"... I have found mercy, taking refuge in the Gospel as the flesh of Jesus and in the Apostles ..." (5:1)
"Yea, and we love the prophets also, because they too pointed to the Gospel in their preaching ... as holy men, approved of Jesus Christ and numbered together in the Gospel of our common hope" (5:2)
"... If I find it not in the charters, I believe it not in the Gospel ..." (8:2)
"But the Gospel has a singular preeminence in the advent of the Saviour, even our Lord Jesus Christ, and His passion and resurrection. For the beloved Prophets in their preaching pointed to Him; but the Gospel is the completion of immortality ..." (9:2)
'To the Smyrnaeans':
"But certain persons ignorantly deny Him, ... and they have not been persuaded by the prophecies nor by the law of Moses, nay nor even to this very hour by the Gospel ..." (5:1)
"... but should give heed to the Prophets, and especially to the Gospel, wherein the passion is shown unto us and the resurrection is accomplished ..." (7:2)

Why would a same author ignore 'gospel' in his first four epistles, then use the word eight times in his fifth & sixth letters combined?
Let's also note the different connotation of the word 'gospel':
In 'to the Philadelphians', its meaning is ambiguous, likely 'Christian message' and does not seem to be about writings. However, in 'to the Smyrnaeans', 'gospel' alludes to book(s), as for the mentioned "prophecies" & "law of Moses", and where the passion & resurrection are described. Once again, why would a common writer give a different signification for the same word?

Notes:
1) The author of 'to the Smyrnaeans' likely knew about GLuke and 'Acts' (& probably GMatthew):
"... He is truly of the race of David according to the flesh, but Son of God by the Divine will and power, truly born of a virgin and baptized by John that all righteousness might be fulfilled by Him [that's according to Mt3:15 "... to fulfill all righteousness ..."]
` from ... truly nailed [Jn20:25?] up in the flesh for our sakes under Pontius Pilate and Herod the tetrarch ..." (1:1-2)
The next quote paraphrases a passage of GLuke (24:36-39):
"... He was in the flesh even after the resurrection; and when He came to Peter and his company, He said to them, Lay hold and handle me, and see that I am not a demon without body ..." (3:2)
And as solely in 'Acts' (10:41):
"And after His resurrection He ate with them and drank with them ..." (3:3)
Another concordance with GMatthew:
6:1 "Let the one who has room for it make room for it"
=> Mt19:12 "Let the one who can make room for it make room for it"
2) The author of 'to the Ephesians' most likely knew about GMatthew:
- 17:1 => Mt26:6-7 (ointment ('myron') upon Jesus' head) (also in Mk14:3)
- 18:2 "Jesus the Christ, was conceived in the womb by Mary ..., of the seed of David but also of the Holy Spirit" => Mt1:18,20 "Joseph, son of David, ... Mary your wife, for that which is conceived in her is of the Holy Spirit." (note: in GLuke (1:32-35) the power of God ("the Most High"), overshadowing Mary, is suggested as a/the conceiver)
- 19:1-2 => Mt2:2-9 (the new star announcing Jesus Christ)
- 5:2 => Mt18:19-20 (two or more, together is better than alone for praying)
- 10:3 => Mt13:25 (plant of the devil/sowed tares of the enemy)
- 14:2 => Mt12:33 (tree known by its fruits)

Note: the three last examples appear to be bits of plagiarism. The same can be said about 16:1 => 1Co6:9-10, Gal5:21 (bad people "shall not inherit the kingdom of God") and 18:1 => 1Co1:20 ("Where is the wise? Where is the disputer?").
Let's also notice the author named Paul and mentioned his past dealing with the Ephesians (12:2).

4.9 Recapitulation and remarks:
First, let's go through a recapitulation per epistle concerning the eight points already addressed.

Legend:
a) N = same author very improbable, N = same author improbable
b) <=> 'contradicted by part(s) of ...'

Considering the above recapitulation, it becomes obvious a common author did not write these letters. More likely (more corroborating evidence to follow), each letter was composed by a different writer, and (except for 'to the Romans' & maybe 'to Polycarp') to his own church.

Note: five of the first six epistles were addressed to churches within an area sixty by eighty miles (see map), along well-travelled routes, making it easy to learn their existence and to collect copies.

However, it is undeniable there are similarities of style between the letters, but also some noticeable differences. And for such small epistles, and knowing about the previous one(s), including the first one & longest (by a lot!), 'to the Ephesians', it would be easy for a subsequent author to imitate the known phraseology.
The book of Isaiah appears to be in the same situation:
Isa1-35 and Isa40-66a have comparable style with numerous similar expressions & words (but mixed with marked distinctions). But very few (if any) critical scholars would vouch for the two parts being written by the same author.
And as a personal experience, I recall the topic of a dissertation during my teenage years. We, I mean students in a technical school (not literary types!), had to write a story in the manner of a renaissance author (Rabelais), in old French. The style & vocabulary of Rabelais are incomparable, I must say. But some (not me!) in our class did very well, without spending much time on the matter.

4.10 More about authorship:

A) Let's observe the progression about "my deacon(s)":
"... my fellow-servant Burrhus, who by the will of God is your deacon blessed in all things, I pray that he may remain with me ..." (Ephes.2:1)
Here, Burrhus, a deacon from Ephesus, is called "my fellow-servant" because Ignatius is fond of him & desires to keep him around. The "my" is therefore understandable.
"Forasmuch then as I was permitted to see you in the person of Damas your godly bishop and your worthy presbyters Bassus and Apollonius and my fellow-servant the deacon Zotion ..." (Magn.2:1)
Why would Ignatius call Zotion, a deacon of Magnesia, "my fellow-servant"? More so when the presbyters are not "his". It seems here the author of that particular epistle "copied" from Ephes.2:1, without taking the context in account.
"... there is one altar, as there is one bishop, together with the presbytery and the deacons my fellow-servants ..." (Philad.4:1)
Now all the deacons of Philadelphia are the personal fellow-servants of Ignatius! That's rather absurd & unsubstantiated but the author obviously took his cues from Ephes.2:1 & Magn.2:1, concluding that deacons were fellow-servants of Ignatius. And not to be outdone, the next author did the same:
"I salute your godly bishop and your venerable presbytery my fellow-servants the deacons ..." (Smyrn.12:2)
A same author could not have drifted into this absurdity.

B) "Am I not able to write to you of heavenly things?" (Trall.5:1)
Why would Ignatius, who allegedly met the bishop, and nobody else from Tralles, defend himself on this subject?
The bishop (whom Ignatius admires) cannot be the one challenging him. Therefore it seems the author went out of character and revealed himself as not being Ignatius. Then, who is the most likely to be accused of that?
The bishop of Tralles, Polybius, more so because Gnosticism was a problem in his community (more on that later, in the next section (#5) "Time of writing").

C) "... Give you heed to the bishop and the presbytery and deacons" (Philad.7:1)
This is allegedly said by Ignatius to the whole Christian community of Philadelphia.
"Give you heed to the bishop, that God also may give heed to you ..." (Polyc.6:1)
That's obviously copied from Philad.7:1, but put in the wrong context here: the addressee is a bishop (& not any bishop at that, the most glorious!). So this exhortation does not make any sense, except, of course, if the letter was not written to Polycarp, but rather as a "pastoral" (& consequently not by Ignatius!).

D) "... Not indeed that I have known of any such thing among you, but I keep watch over you betimes, as my beloved, for I foresee the snares of the devil ..." (Trall.8:1)
Here, Ignatius would have known of a community in peace, but foresee, in the future, the devil, that is the intrusion of Gnostic beliefs (as explained in section 5, the next one). That indicates a significant amount of time elapsed between the alleged trip to martyrdom and the writing of this epistle. The same goes for the next quote:
"But these things I warn you, dearly beloved, knowing that you yourselves are so minded. Howbeit I watch over you betimes to protect you from wild beasts in human form -- men whom not only should you not receive ..." (Smyrn.4:1)
This passage is drawn from Trall.8:1 "beloved ... watch over you betimes" and rewritten. Again, it is a warning against Gnostics to come (as shown in section 5).

E) Some characteristics of the bishops allegedly met by Ignatius are rather unexpected:
"And in proportion as a man says that his bishop is silent, let him fear him the more ..." (Ephes.6:1)
It is suggested here, Onesimus, the bishop of Ephesus, was rather silent. It seems Onesimus was very discreet and removed (at the time of Ignatius' alleged trip). Maybe few persons knew he was a bishop then!
"Yea, and it becomes you also not to presume upon the youth of your bishop ..." (Magn.3:1)
A young bishop! That's very odd. Or maybe Damas was middle-aged at the writing of the letter, therefore a young man during Ignatius' last year!
"... And I am amazed at his forbearance; whose silence is more powerful than others' speech." (Philad.1:1)
Another silent bishop: same comments as for Ephes.6:1.

4.11 The five churches:
If, along several months or years, different writers, who knew (except for the first one, of course) about the earlier Ignatian epistle(s), issued a letter to their respective church, then the particular "Catholic" faith (existing or wished for) in each of these Christian communities can be specified as such (besides Jesus' death & resurrection):
Ephesians:
a) Jesus as the God of the Christians (but NO mention of pre-existence)
b) Jesus as Christ (33 times), Lord (9 times), Saviour (1:1), the son of Mary (7:2,18:2,19:1), Son of God (4:4,7:2,20:2), Son of David (18:2), Son of Man (20:2)
c) The virgin conception (19:1)
d) "These are the last times. Henceforth let us have reverence; let us fear the long-suffering of God, lest it turn into a judgment against us. For either let us fear the wrath which is to come ..." (11:1)
Magnesians:
a) Jesus as NOT the God of the Christians but pre-existent (6:1,7:2,8:2) as the Word (8:2)
b) Jesus as Christ (21), Lord (2), Saviour (0:0), Son of God (8:2,13:1)
c) Probably not the virgin conception
d) "[Jesus] appeared at the end of time" (6:1)

Note: the next five letters never allude to "the last times", or "the end of time" or, more generally, to a future DAY of the Lord.

Note: these beliefs are very basic (primitive), making the Christians there an easy prey for Gnostics (see next section).

Note: the last point is a repeat from Magn.9:2 and likely a new import.

5. Time of writing:

5.1 Attack against Gnostics:
"But if it were as certain persons who are godless, that is unbelievers, say, that He suffered only in semblance, ..." (Trall.10:1)
"... He suffered truly, as also He raised Himself truly; not as certain unbelievers say, that He suffered in semblance ..." (Smyrn.2:1)
Some early Gnostics preached Jesus was not crucified, just someone else in his semblance:
As reported by Irenaeus, about Basilides (120-140), AH, I, 24, 4 "[Basilides thought] ... he did not himself suffer death, but Simon, a certain man of Cyrene, being compelled, bore the cross in his stead, so that this latter being transfigured by him, that he might be thought to be Jesus, was crucified, ..., while Jesus himself received the form of Simon, and, standing by, laughed at them."
Those Gnostics denied Jesus' death:
"... His death which some men deny ..." (Magn.9:1)
This is why it had to be believed:
"... that believing on His death you might escape death." (Trall.2:1)
Allowing some time for this Gnostic doctrine to have an impact in Asia minor, these letters could not have been written before 125-130.

Note: another allusion to Basilides' doctrine:
"Am I not able to write to you of heavenly things? ... For I myself also, albeit I am in bonds and can comprehend heavenly things and the arrays of the angels and the musterings of the principalities, things visible and things invisible ..." (Trall.5:1-2)
As reported by Irenaeus, about Basilides, AH, I, 24, 3 "Basilides again, that he may appear to have discovered something more sublime and plausible, gives an immense development to his doctrines. He sets forth that Nous was first born of the unborn father, that from him, again, was born Logos, from Logos Phronesis, from Phronesis Sophia and Dynamis, and from Dynamis and Sophia the powers, and principalities, and angels, whom he also calls the first; and that by them the first heaven was made. Then other powers, being formed by emanation from these, crated another heaven similar to the first; and in like manner, when others, again, had been formed by emanation from them, corresponding exactly to those above them, these, too, framed another third heaven; and then from this third, in downward order, there was a fourth succession of descendants; and so on, after the same fashion, they declare that more and more principalities and angels were formed, and three hundred and sixty-five heavens."
Remark: Ignatius, or rather Polybius, did not want to be outdone about understanding the heavens!

5.2 Christians preventing the execution:
In 'to the Romans', it is feared the Christians of Rome would prevent Ignatius' execution ("in bonds for the sake of the common Name" (Ephes.1:2), that is convicted of being a Christian). But how, if not by the emperor's intervention or/and a judicial process?
During Hadrian's reign (117-138), Christians started to address apologies to the emperor, for the purpose of defending their faith & avoiding persecutions. Two of those we know are from Aristides and Quadratus, who wrote them around 125-130.
Also, according to Justin Martyr, 1Apology, 68 (written 150-160), Hadrian forbid persecution of Christians without trial. And if prosecuted, they had to be proven guilty of illegalities:
"... [in order not] the men [Christians] be harassed and opportunity be given to the informers for practicing villainy. If, therefore, the inhabitants of the province can clearly sustain this petition against the Christians so as to give answer in a court of law, let them pursue this course alone, but let them not have resort to men's petitions and outcries. ... If any one therefore accuses them and shows that they are doing anything contrary to the laws, do you pass judgment according to the heinousness of the crime ..."
However, the practice of slaying Christians just to please the populace (or local authorities) was acceptable during Hadrian's predecessor, Trajan:
"... it is not possible to lay down any general rule to serve as a kind of fixed standard. They are not to be sought out; if they are denounced and proved guilty [of being Christians, not of crimes!], they are to be punished [which according to Pliny's letter is by execution!], with this reservation, that whoever denies that he is a Christian and really proves it--that is, by worshiping our gods--even though he was under suspicion in the past, shall obtain pardon through repentance." (Trajan's reply to Pliny the Younger)
Therefore, the Christians of Rome being able to prevent Ignatius' execution (by appealing to the emperor or/and asking for a trial) is plausible during Hadrian's rule, but not for Trajan's reign.
Once again, a dating of not earlier than 125-130 would be called for.

5.3 Polycarp:
The best way to explain the fact that 'Polycarp' is ignored in 'to the Smyrneans' (and others letters written from Smyrna), while he is glorified in 'to Polycarp', is to postulate there was a significant amount of years between the writing of the last letter and the others. It seems 'to the Smyrnaeans' (and previous epistles) was written when Polycarp had not emerged yet as the preeminent Christian of Smyrna and its bishop (more corroborating evidence against early bishops in next section).
But Polycarp is supposed to have been a bishop since the late 1st century, according to Irenaeus (AH, III, 3, 4)!
However Irenaeus knew only Polycarp when the later was an old man:
"Polycarp ... bishop of the Church in Smyrna, whom I also saw in my early youth, for he tarried a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom ..." (AH, III, 3, 4)
And Irenaeus can only relate about the later years of Polycarp' activities, such as his meetings with "heretic" Marcion (from 140-145) & Anicetus (bishop of Rome from around 156) and attacks against Gnostics.
So the following might be strictly legendary:
"But Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna ..." (AH, III, 3, 4)
More so because in Polycarp's own letter 'to the Philippians', the author does not suggest his old (but important) acquaintances, or he is a bishop.

Note: the fairly detailed account of Polycarp's martyrdom was supposedly written right after the event (but probably later, in account of the obvious embellishments). In it, Polycarp is declared to be "a bishop" only once, and that appears towards the end (16:2).

Therefore, it seems the first six letters were written before Polycarp's preeminence, while the last one was composed either during Polycarp's last years or, more likely, after his execution.

Conclusion:
A dating of around 135 (plus/minus 10 years) for the seven epistles (except the last) seems reasonable. 'To Polycarp' was probably written soon after 155-167.

6. About the earliest bishops:

6.1 Ignatius as bishop:
As already mentioned in the introduction, in all of the seven epistles of the middle recension, Ignatius is declared a bishop only in the fourth letter, 'to the Romans'.
This letter is the most unique among the Ignatian epistles and considerably "over the top". Its main theme, unlike for the others, revolves around the sublimeness of Christian martyrdom and the glorification of Ignatius. And among the "seven", it is the most contested (with 'to Polycarp') as being authentic.
Here is the only passage which identifies Ignatius as a bishop:
"... for that God has vouchsafed that the bishop from Syria should be found in the West, having summoned him from the East" (2:2b)
That's rather "in passing". In the same letter, 'Ignatius as a bishop' is also implied here:
"... the church which is in Syria, which has God for its shepherd in my stead. Jesus Christ alone shall be its bishop -- He and your love." (9:1)
How could the author know Ignatius was a bishop, but not be able to name his city? More so because a bishop, in the Ignatian letters, is based in (& identified by) a city.
And why would Ignatius not be declared a bishop in the preceding letters, since the virtue & importance of bishopry are extolled here?
Let's see how Ignatius is described in those epistles:
"... now am I beginning to be a disciple; and I speak to you as to my school-fellows ..." (Ephes.3:1)
"the church which is in Syria, whence I am led a prisoner to Rome -- I who am the very last of the faithful there;" (Ephes.21:1)
"the church which is in Syria, whereof I am not worthy to be called a member" (Magn.14:1)
"... Remember in your prayers the church which is in Syria; whereof I am not worthy to be called a member, being the very last of them." (Trall.13:1)

Note: probably for sake of continuity, this denigrating statement ("... being the very last of them ...") is repeated in Rom.9:2.

"Not worthy to be called a member, being the very last of them" does not describe a bishop, rather depicts someone at the lowest echelon in the Christian community! Would it be (false) modesty?
Certainly Ignatius is not shown low-key in 'to the Romans'; and in 'to Polycarp' he tells "godly" bishop Polycarp what to do and be! Furthermore, if Ignatius was known as a bishop then, such statements would considerably demean the position, more, ridicule it, whereas in the letters (except 'to the Romans') the quasi-worshipping of the local bishop is exhorted:
"... Plainly therefore we ought to regard the bishop as the Lord Himself" (Ephes.6:1)
"... the bishop presiding after the likeness of God ..." (Magn.6:1)
"... cheer the soul of your bishop unto the honour of the Father ..." (Trall.12:2)

The first three epistles rather dismiss Ignatius as a bishop and it is very unlikely he was known then as such.
What about the last three letters?
They do not mention Ignatius as a bishop, but neither they reproduce the demeaning statements (except in Smyrn.11:1). But they specify 'Antioch'!

But then, why would Ignatius become a bishop in the fourth letter?
Let's start by saying, in the first three epistles, a bishop is presented as almost being Christ (or even God). And in 'to the Romans' Ignatius is elevated to unprecedented heights (with some help from Paul's epistles!):
"... I am a word of God ..." (2:1)
"... I may be found a sacrifice to God [as Christ!] ..." (4:2)
"From Syria even unto Rome I fight with wild beasts,
[as for Paul in 1Co15:32: "... I have fought with beasts ..."]
` by land and sea, by night and by day, being bound amidst ten leopards, even a company of soldiers
[as a superlative gladiator or another Daniel (as in the lions' pit)!] ..." (5:1)
"The farthest bounds of the universe shall profit me nothing [a cosmic-wide view!], neither the kingdoms of this world. It is good for me to die for Jesus Christ rather than to reign over the farthest bounds of the earth
[as if becoming the emperor of the world would be an option for Ignatius! Likely inspired from Mt4:8-10 &/or Lk4:5-8, where all the earthly kingdoms are offered to Christ!] ..." (6:1)
"Permit me to be an imitator of the passion of my God
[as for Paul in Php3:10: "that I may know ... the fellowship of His sufferings, being conformed to His death"] ..." (6:3)
The greatly enhanced status in 'to the Romans' would explain Ignatius' elevation to bishop: the God-sized superlative martyr could not just be a lesser member of a church! Furthermore, the martyrdom of the leader of Syrian Christians is a lot more significant than the one of a lowly believer!
"... I be poured out a libation to God,
[as for Paul in Php2:17: "... I am being poured out as a drink offering ..."]
` while there is still an altar ready; that forming yourselves into a chorus in love you may sing to the Father in Jesus Christ, for that God has vouchsafed that the bishop from Syria should be found in the West, having summoned him from the East. It is good to set from the world unto God, that I may rise unto Him
[as for Paul in Php3:11: "... I may attain to the resurrection from the dead ..."]." (Rom.2:2)

Notes:
a) Because 'to the Romans' has little theological value (except specifying Jesus as the only Son --0:0), is not meant to edify the Romans, but is rather about glorifying Ignatius & martyrdom, it is probable this epistle was issued in Asia minor.
b) The motives & authorship behind 'to the Romans' might be the same ones as for the 'Acts of Paul & Thecla', written 150-200:
According to Tertullian, 'On Baptism',17 "But if the writings which wrongly go under Paul's name, claim Thecla's example as a licence for women's teaching and baptizing, let them know that, in Asia, the presbyter who composed that writing, as if he were augmenting Paul's fame from his own store, after being convicted, and confessing that he had done it from love of Paul, was removed from his office."
Despite the conviction, the 'Acts of Paul & Thecla' were highly regarded early on:
"The Acts of Paul were by far the most popular of the apocryphal acts, spawning a great deal of Christian art and secondary literature, as well as a cult which venerated Thecla, the young girl who accompanies Paul on his missionary journeys. The Acts were considered orthodox by Hippolytus, as well as other writers as late as the mid-fourth century, but were eventually rejected by the church when heretical groups like the Manichaeans began to adopt them." Geoff Trowbridge, Introduction of the 'Acts of Paul'

Ignatius, as a bishop, was likely very much doubted, because the last three letters (and Irenaeus) do not mention it. The earliest "corroboration" comes some one hundred years later, by Origen (as the successor of Peter!). One more century later, Eusebius had him succeeding Evodius (& not Peter!), and mentioned Ignatius' successor:
"There we must leave Ignatius. As bishop of Antioch he was succeeded by Hero." (HC, 3, 36)
which apparently went against Ignatius' wishes!
"... the church which is in Syria, which has God for its shepherd in my stead. Jesus Christ alone shall be its bishop ..." (Rom.9:1)

6.2 Bishop(s) in the N.T.:
The word for 'bishop' (Greek 'episkopos') normally means, according to Strong:
"1) an overseer
1a) a man charged with the duty of seeing that things to be done by others are done rightly, any curator, guardian or superintendent
1b) the superintendent, elder, or overseer of a Christian church"
As we can see, 'bishop' is far for being its primary meaning.
The word appears first in Christian texts as such:
"For it will be no small sin in us if we depose from the office of bishop those who blamelessly and piously have made the offerings. Happy are the presbyters who finished their course before, and died in mature age after they had borne fruit; for they do not fear lest any one should remove them from the place appointed for them." (1Clement,ch.44, written 80-81--my dating)
Here, bishop and presbyter seem to be interchangeable. This is confirmed next:
"And thus preaching through countries and cities, they [apostles] appointed the first-fruits, having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe." (1Clement,ch.42)

Notes:
a) "Clement" justified "bishops" and "deacons" not by direct examples, but by quoting (with mistranslation!) a passage from the O.T.:
"Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture in a certain place, "I will appoint their bishops in righteousness, and their deacons in faith."" (1Clement,ch.42)
The closest scripture is from the LXX version of Isaiah60:17:
"... I will give thy rulers in peace, and thy overseers in righteousness ..."
However the Hebrew Bible is translated as such:
"Instead of bronze I will bring gold, and instead of iron I will bring silver, and instead of wood, bronze, and instead of stones, iron. And I will make peace your administrators and righteousness your overseers
[peace and righteousness will replace (human) administrators & overseers in the new Zion.
We are a long way from appointments of bishops & deacons!]." NASB
b) According to Strong, the word 'deacon' (Greek 'diakonos') has for main meaning:
"one who executes the commands of another, esp. of a master, a servant, attendant, minister"

It is clear here 'bishops' means overseers only, and not necessarily over deacons, possibly over laymen only.
"bishops" and "deacons" are also seen in canonical writings.
Here are all of the four occurrences of 'bishop(s)'/'overseer(s)' in the N.T.:
a) "Therefore take heed to yourselves [the elders of the church of Ephesus (20:18-19)] and to all the flock, among which the Holy Spirit has made you overseers ..." (Ac20:28a, written circa.90)

Note: according to Strong, for the definition of 'presbuteros', "The NT uses the term bishops, elders, and presbyters interchangeably"

b) "To all the saints in Christ Jesus who are in Philippi, with the bishops and deacons:" (Php1:1)
Once again, those bishops seem to be presbyters.

Note: was it written by Paul? Likely not, because 'Philippians' is a combination of three letters which required a new common introduction. Furthermore, NONE of the generally considered genuine (seven) epistles of Paul (Ro,1/2Co,Gal,Php,1Th,Phm) has the word 'bishop(s)' in them.

c) "This is a faithful saying: If a man desires the position of a bishop, he desires a good work. A bishop then must be blameless, the husband of one wife, temperate, sober-minded, of good behavior, hospitable, able to teach; not given to wine, not violent, not greedy for money, but gentle, not quarrelsome, not covetous; one who rules his own house well, having his children in submission with all reverence ... not a novice ..." (1Ti3:1-6a, written circa.125)
Next, the author reviewed the qualifications for deacons (3:8-13). It is obvious here this bishop is a presbyter, as confirmed by the following, which is largely copied from '1Timothy':
d) "For this reason I left you in Crete [Titus, allegedly acting as a true bishop], that you should set in order the things that are lacking, and appoint elders in every city as I commanded you-- if a man is blameless, the husband of one wife, having faithful children not accused of dissipation or insubordination. For a bishop must be blameless, as a steward of God, not self-willed, not quick-tempered, not given to wine, not violent, not greedy for money" (Tit1:5-7, written circa.125)
Here elders (presbyters) are the same as bishops.

As we can see, the usage of 'bishop(s)'/'overseer(s)' for presbyters/elders denies the word 'bishop' ('episkopos') was thought then as the Christian leader in one city. And because of the aforementioned meaning of 'bishops', it is very difficult to imagine true bishops existed at this time, contrary to later claims (see 6.3 next)
However, the treatment of Timothy and Titus in the "Pastorals", written in the first part of the 2nd century, foresees true bishops (and was probably the origin of apostles appointing "real" bishops).

6.3 About the early "Catholic" bishops:

6.3.1 From Hegesippus:
Hegesippus (wrote 165-180), a converted Jew with some Jewish Christian beliefs, was probably the first to mention (true) bishops and an uninterrupted continuity from the very beginning:
"And the church of the Corinthians continued in the orthodox faith up to the time when Primus was bishop in Corinth. I had some intercourse with these brethren on my voyage to Rome, when I spent several days with the Corinthians, during which we were mutually refreshed by the orthodox faith.
On my arrival at Rome, I drew up a list of the succession of bishops down to Anicetus,
[but the list (with its first bishop) is not given!]
` whose deacon was Eleutherus. To Anicetus succeeded Soter, and after him came Eleutherus.
[the following seems to be a vague generalization motivated by wishful thinking: let's notice the importance given to the Mosaic law and the prophets!]
` But in the case of every succession,
[that is, according to the context (see next), 'under each one of the successive bishops']
` and in every city, the state of affairs is in accordance with the teaching of the Law and of the Prophets and of the Lord ..." (HC, 4, 22)
From Hegesippus again:
"And after James the Just had suffered martyrdom, as the Lord had also on the same account, Symeon, the son of the Lord's uncle, Clopas, was appointed the next bishop. All proposed him as second bishop because he was a cousin of the Lord." (HC, 4, 22)
Here, James, Jesus' brother, is implied to be the first bishop of Jerusalem. But according to Paul's letters, more so 'Galatians', this James is only one of three named "pillars" of the church there (Gal2:9). 'Acts' and 'James' do not give James any title. However, he had some preeminence there, enough to be considered a bishop (posthumously!).
That's all we have about bishop(s) from Hegesippus.

6.3.2 From Dionysius:
Another Church writer in these days (165-175) was Dionysius, the bishop of Corinth. According to Eusebius (HC, 4, 23), this Dionysius "revealed" (for the first time) three early bishops of Athens (starting from a convert of Paul) and named several bishops as his contemporaries: Soter of Rome, Philip of Gortyna (Crete), Palmas of Amastris (Pontus) and Pynetus (Cnossians). Eusebius also wrote:
"There is also extant an epistle of Dionysius to the Romans, addressed to the then bishop, Soter ..."

Note: it makes sense an epistle to the Romans would be first sent to the bishop. That's in contrast with the Ignatian epistle, 'to the Smyrnaeans', which put the local (unnamed) bishop "out of the loop" (11:2)!

6.3.3 From Irenaeus:
Then we arrive to Irenaeus (wrote 170-180). In 'Against Heresies', he devoted several sections "proving" the uninterrupted continuity of the Christian message (involving bishops), as a line of defence against "heretics". Here is a relevant passage from 'Against Heresies', book 3, chapters 2 & 3:

Ch.2, 1 "When, however, they [heretics] are confuted from the Scriptures, they turn round and accuse these same Scriptures, as if they were not correct, nor of authority, and [assert] that they are ambiguous, and that the truth cannot be extracted from them by those who are ignorant of tradition. For [they allege] that the truth was not delivered by means of written documents, but vivā voce: wherefore also Paul declared, "But we speak wisdom among those that are perfect, but not the wisdom of this world." And this wisdom each one of them alleges to be the fiction of his own inventing, forsooth; so that, according to their idea, the truth properly resides at one time in Valentinus, at another in Marcion, at another in Cerinthus, then afterwards in Basilides, or has even been indifferently in any other opponent, who could speak nothing pertaining to salvation. For every one of these men, being altogether of a perverse disposition, depraving the system of truth, is not ashamed to preach himself.

2 But, again, when we refer them to that tradition which originates from the apostles, [and] which is preserved by means of the succession of presbyters in the Churches, they object to tradition, saying that they themselves are wiser not merely than the presbyters, but even than the apostles, because they have discovered the unadulterated truth. For [they maintain] that the apostles intermingled the things of the law with the words of the Saviour; and that not the apostles alone, but even the Lord Himself, spoke as at one time from the Demiurge, at another from the intermediate place, and yet again from the Pleroma, but that they themselves, indubitably, unsulliedly, and purely, have knowledge of the hidden mystery: this is, indeed, to blaspheme their Creator after a most impudent manner! It comes to this, therefore, that these men do now consent neither to Scripture nor to tradition.

3 Such are the adversaries with whom we have to deal, my very dear friend, endeavouring like slippery serpents to escape at all points. Where-fore they must be opposed at all points, if per-chance, by cutting off their retreat, we may succeed in turning them back to the truth. For, though it is not an easy thing for a soul under the influence of error to repent, yet, on the other hand, it is not altogether impossible to escape from error when the truth is brought alongside it."

Ch.3, 1 "It is within the power of all, therefore, in every Church who may wish to see the truth, to contemplate clearly the tradition of the apostles manifested throughout the whole world; and we are in a position to reckon up those who were by the apostles instituted bishops in the Churches, and the succession of these men to our own times; those who neither taught nor knew of anything like what these [heretics] rave about.
For if the apostles had known hidden mysteries, which they were in the habit of imparting to "the perfect" apart and privily from the rest, they would have delivered them especially to those to whom they were also committing the Churches themselves. For they were desirous that these men should be very perfect and blameless in all things, whom also they were leaving behind as their successors, delivering up their own place of government to these men;
[the earliest generations of Christians thought the kingdom of God would come in their lifetime and did not have any long term plan, such as setting up succession. Paul, for example, wrote:
"Because of the present crisis, I think that it is good for you to remain as you are ... Are you unmarried? Do not look for a wife ..." (1Co7:26-27)
"But this I say, brethren, the time has been shortened, so that from now on those who have wives should be as though they had none;" (1Co7:29)]

` which men, if they discharged their functions honestly, would be a great boon, but if they should fall away, the direst calamity.
[the argument: if the apostles confided secrets to their best faithful, then selecting those to be the first bishops, these mysteries, transmitted through succession, would be a great asset for the Church then.
Now what remains to be demonstrated in the uninterrupted succession. If "proven", then the Gnostics would lose their argument about the original "hidden secrets" not getting transferred to the late 2nd cent. "Catholic" Church (but to them instead!). More to come ...]

2 Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches,
[in '1Clement' there is NO indication the Corinthians had one city-wide bishop. If a local bishop existed, he could not have been ignored. The same remark goes for Polycarp's letter addressed to the Philippians: NO bishop here either]

` we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized [Gnostic!] meetings;
[here comes the main argument: uninterrupted continuity from Paul & Peter]

` by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul;
[Paul & Peter founding jointly the church in Rome is strictly legendary ('Peter in Rome' is very suspect: see later):
A) According to Paul's own letter 'Romans', a thriving Christian community existed in Rome well before Paul went there.
B) Paul had a public feud in Antioch (52C.E.) with Peter (Gal2:10-14) over the issues of 'Jewish customs upon Gentiles' and obedience to James (Jesus' brother). This dispute is never reported to have been resolved. Certainly, according to the content of 'Galatians' & 'Romans', the gap seems to have become wider, not narrower, that is between Pauline Christianity and Judaism.
C) 'Peter in Rome' is first "revealed" by Dionysius of Corinth more than three generations later (circa.170):
"... the churches that were planted by Peter and Paul, that of the Romans and that of the Corinthians: for both of them went to our Corinth, and taught us in the same way as they taught you when they went to Italy; and having taught you, they suffered martyrdom at the same time."
This epistle was sent to (& praising) the Roman bishop, Soter, and probably meant to help him out against heretics: "... you Romans, keep up the custom of the Romans handed down by the fathers, which your blessed Bishop Soter has not only preserved, but added to [oh! bad choice of words!]..."
Let's notice the Romans (not bishops) transmitting the "custom" from the fathers, with Soter as the first bishop keeping it (in his mind, I guess, because Soter is not known to have written anything). Later, Irenaeus will have the same handed down from one bishop to the next, starting by Peter & Paul!
This seems an extrapolation of the (written circa. 135) Ignatian letter 'to the Romans':
4:3 "I do not, as Peter and Paul [putting out orders, generally speaking, but likely not from Rome, as shown next], issue [in this context, for Ignatius, NOT from Rome!] commandments unto you. They were apostles of Jesus Christ ... they were free [unlike Paul in Rome, according to 'Acts'!]"
It is itself a likely elaboration from (written circa. 80) '1Clement':
ch.42 "The apostles have preached the Gospel to us [here, according to the context, "us" means early Christians generally] from the Lord Jesus Christ"
Let's notice the progression from '1Clement', then 'to the Romans', then Dionysius & finally to Irenaeus!
D) '1Clement', written much earlier, does not specify martyrdom for Peter & Paul, nor their death together or in Rome:
5:2-7 "Let us take the noble examples of our own generation. Through jealousy and envy the greatest and most just pillars of the Church were persecuted, and came even unto death. Let us place before our eyes the good Apostles.
Peter, through unjust envy, endured not one or two but many labours, and at last, having delivered his testimony, departed unto the place of glory due to him.
Through envy Paul, too, showed by example the prize that is given to patience: seven times was he cast into chains; he was banished; he was stoned; having become a herald, both in the East and in the West, he obtained the noble renown due to his faith; and having preached righteousness to the whole world, and having come to the extremity of the West,
["Clement" seemed to rule out Paul's death in Rome, but rather in Spain (as likely extrapolated from Ro15:24,28, because it was Paul's wish to go to Spain)]
` and having borne witness before rulers, he departed at length out of the world, and went to the holy place, having become the greatest example of patience."
Caution: some translations specify death by martyrdom for Peter & Paul. This is NOT correct according to the Greek, just zealous interpretation.
E) 'Acts' does not say Peter went with Paul to Italy, though Paul's trip to Rome & the first two years there (under house arrest) are described with details.
'Peter in Rome' might have originated from '1Peter', an epistle allegedly written from "Babylon" (5:13). But if 'Babylon' meant 'Rome' (from 70C.E., after the Romans totally destroyed Jerusalem, as the Babylonians did centuries before), then Peter could not have been martyred with Paul (that is before 70)! (remark: it is clear, according to the epistle itself, that the author knew his audience thought Peter may be still alive then)
F) Irenaeus is the first witness of the following passage in 'Galatians':
Gal2:7-8 "... when they saw that the gospel for the uncircumcised had been committed to me [Paul], as the gospel for the circumcised was to Peter (for He who worked effectively in Peter for the apostleship to the circumcised also worked effectively in me toward the Gentiles),"
Paul called "Stone" as "Cephas" (1Co1:12,3:22,9:5,15:5, Gal1:18,2:9,11,14). But there are two exceptions: "Peter" appears twice in Gal2:7-8. For many reasons (& not only because of 'Peter'), Gal2:7-8 (except for "On the contrary") is very likely a later interpolation. See http://www.depts.drew.edu/jhc/barnikol.htm for details]

` as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church,
[of Rome --this is the first time the primacy of that church is clearly claimed]

` on account of its preeminent authority -- that is, the faithful everywhere -- inasmuch as the Apostolic Tradition has been preserved continuously by those who are everywhere.
[now, in order to "prove" the sacred continuity, the succession in Rome is spelled out]

3 The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. Of this Linus, Paul makes mention in the Epistles to Timothy.
[as a name among others, and not even the first one of the list: "Eubulus greets you, as well as Pudens, Linus, Claudia, and all the brethren." (2Ti4:21). If this Linus had been selected by Paul as the bishop of Rome (or even self-appointed), a placement on top of the list would be expected]

` To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric. This man, as he had seen the blessed apostles, and had been conversant with them, might be said to have the preaching of the apostles still echoing [in his ears], and their traditions before his eyes.
[the claim that Clement knew & conversed with the apostles is unsubstantiated. '1Clement', presumably written by Clement, does not even suggest that. Furthermore, most apostles then (as Paul) never met the earthly Jesus, but allegedly only the heavenly one (through the Spirit & revelations!):
"But I make known to you, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but it came through the revelation of Jesus Christ." (Gal1:11-12)
"It is doubtless not profitable for me to boast. I will come to visions and revelations of the Lord:" (2Co12:1)
"But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God." (1Co2:10)
And all the very first apostles did not agree with each other; Paul was bitter against "false apostles":
"... those who desire an opportunity to be regarded just as we are in the things of which they boast. For such are false apostles, deceitful workers, transforming themselves into apostles of Christ." (2Co11:12-13)
and those preaching different 'Jesus' & gospels:
"For if he who comes preaches another Jesus whom we have not preached, or if you receive a different spirit which you have not received, or a different gospel which you have not accepted--you may well put up with it! For I consider that I am not at all inferior to the most eminent apostles. Even though I am untrained in speech, yet I am not in knowledge ..." (2Co11:4-6)
"I marvel that you are turning away so soon from Him who called you in the grace of Christ, to a different gospel, which is not another; but there are some who trouble you and want to pervert the gospel of Christ ... As we have said before, so now I say again, if anyone preaches any other gospel to you than what you have received, let him be accursed." (Gal1:6-9)
The visit to Corinth by Peter & Apollos (not even "false" apostles!) divided the Christian community there:
"For it has been declared to me concerning you, my brethren, by those of Chloe's household, that there are contentions among you. Now I say this, that each of you says, "I am of Paul," or "I am of Apollos [NO apostle, just a preacher/teacher!]," or "I am of Cephas [Peter]," or "I am of Christ."" (1Co1:11-12)
And when Paul was in jail, some replacements were not commendable (and certainly not selected by Paul!):
"Some indeed preach Christ even from envy and strife, and some also from goodwill: The former preach Christ from selfish ambition, not sincerely, supposing to add affliction to my chains;" (Php1:15-16)]

` Nor was he alone [in this], for there were many still remaining who had received instructions from the apostles. In the time of this Clement, no small dissension having occurred among the brethren at Corinth, the Church in Rome dispatched a most powerful letter to the Corinthians,
[it seems Irenaeus knew about Clement only by the aforementioned letter and nothing else. In '1Clement', the author never wrote he is Clement or a bishop]

` exhorting them to peace, renewing their faith, and declaring the tradition which it had lately received from the apostles,
["Clement" knew about some of Paul's letters, 'Hebrews' and likely GMark. His letter quotes the aforementioned works, plus the Septuagint. However, "Clement" never claimed he learned first hand from the apostles]

` proclaiming the one God, omnipotent, the Maker of heaven and earth, the Creator of man, who brought on the deluge, and called Abraham, who led the people from the land of Egypt, spoke with Moses, set forth the law, sent the prophets, and who has prepared fire for the devil and his angels.
[Jewish & Christian beliefs that the Gnostics rejected. Irenaeus used '1Clement' as a "spot check"]

` From this document, whosoever chooses to do so, may learn that He, the Father of our Lord Jesus Christ, was preached by the Churches, and may also understand the apostolic tradition of the Church, since this Epistle is of older date than these men who are now propagating falsehood, and who conjure into existence another god beyond the Creator and the Maker of all existing things. To this Clement there succeeded Evaristus. Alexander followed Evaristus; then, sixth from the apostles, Sixtus was appointed; after him, Telephorus, who was gloriously martyred; then Hyginus; after him, Pius;
[the existence of these aforementioned 2nd cent. bishops is first revealed here. Let's note we have NO evidence (or mention) of a single writing from them (also true for the four next ones)]

` then after him, Anicetus. Soter having succeeded Anicetus, Eleutherius does now, in the twelfth place from the apostles, hold the inheritance of the episcopate. In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us. And this is most abundant proof that there is one and the same vivifying faith, which has been preserved in the Church from the apostles until now, and handed down in truth." (AH, 3, 1-3)

Essentially, a succession of bishops from jointly Paul & Peter in Rome (very dubious!) is the only "proof" the transmitted traditions are the right ones. To satisfy this crucial argument, bishops are brought up, some whose names were unknown before in Christian writings, others whose name appeared here or there, but not as bishops (that is, before Irenaeus!).
This is flawed & suspicious evidence for early successive empowered (true) bishops, more so because the Ignatian letter, 'to the Romans', ignores the existence of a Roman bishop then. And in all his available works, apologist Justin, who lived in Rome in the mid-2nd century, never wrote anything about bishop(s). Instead, the Sunday gathering of Christians that Justin attended were led by a "president of the brethen" (1Apology, LXV & LXVII).

6.3.4 From Eusebius:
Eusebius, writing around 315 his 'History of the Church', came up with lists of bishops in Rome, Jerusalem, Alexandria and Antioch (with a detailed dating for the earliest ones of Rome & Alexandria!).
He quoted also a tale published by Clement of Alexandria (wrote circa.190) whereas John the apostle, after 96, appointed bishops in Asia (HC, 3, 23). Also, in HC, 2, 25:
".. Paul was beheaded in Rome itself, and that Peter likewise was crucified under Nero.
[Tertullian, writing around 210-220, was the first to specify the mode of execution for Peter and put it under Nero. But GMark does not seem to be aware of that when it implies (in 13:14,21,23) some disciples (including Peter) were in Judea in 70C.E. (& consequently outlasted Nero!). Furthermore, in the original version of GJohn (written around 75-80), the apostles, including Peter, are still believed to be alive:
Jn14:2-3 "In My Father's house are many mansions; if it were not so, I would have told you [the disciples]. I go to prepare a place for you. And if I go and prepare a place for you, I will come again and receive you to Myself; that where I am, there you may be also."
And the beheading of Paul under Nero is first told in 'Acts of Paul', written 150-200 in Asia minor, by a convicted forger, "augmenting Paul's fame from his own store", as explained earlier]
` This account of Peter and Paul is substantiated by the fact that their names are preserved in the cemeteries
[who would have collected the bodies and buried them? Persecuted Christians?]
` of that place even to the present day. It is confirmed likewise by Caius, a member of the Church, who arose under Zephyrinus, bishop of Rome.
[circa.210! Why were they not found or reported before? Tertullian lived for years (circa.180) in Rome but did not say he saw these tombs himself!]
` He, in a published disputation with Proclus, the leader of the Phrygian heresy, speaks as follows concerning the places where the sacred corpses of the aforesaid apostles are laid: "But I can show the trophies [monuments] of the apostles. For if you will go to the Vatican or to the Ostian way, you will find the trophies of those who laid the foundations of this church."

Note: let's notice no details have been postulated by the fathers about Peter's alleged sejourn(s) in Rome; and considering Peter's preaching & martyrdom in Rome are not divulged before circa.170 (by Dionysius of Corinth!), his founding & organizing (with Paul!) of the Roman church not mentioned before circa.180 (by Irenaeus of Lyons), his crucifixion & tomb in Rome not revealed before circa.210 (by Caius, not even a bishop), we have to wonder about the uninterrupted transmission of traditions by the Roman bishops!
If Peter's execution in Rome is true, then Irenaeus' big argument is considerably weakened, if not defeated!
If untrue, then it shows that "traditions" can be fabricated along the way, bishops or no bishops (as for Jesus' birth on December 25th, in the 4th century!).
The later hypothesis is likely the valid one, because the transmissions by successive generations of Roman Christians (not necessarily bishops) apparently did not include Peter's visit to Rome & his death here. That was brought up very late by other Christian writers in their fight against unorthodox/heretic/gnostic doctrines, in order to provide them with so-called evidence (as for the existence of early "whole city" bishops).

7. Last remarks and conclusion:

Considering:
a) The word 'bishop' (Greek 'episkopos') was used up to circa.125 in a different meaning than 'leader of the city-wide church'.
b) The existence of the early bishops is uncorroborated by '1Clement' (80-81) & 'Polycarp to the Philippians' (circa.135). And the Ignatian epistle 'to the Romans' (circa.135) ignores any bishop there.
c) The lists of early bishops are suspect and likely produced to counteract heretics by invoking uninterrupted continuity (from dubious origins, such as Paul & Peter founding jointly the church in Rome!).
Then the existence of true city-wide bishops before 125 not only can be contested, but also justifiably dismissed, although some early Christians of mark (more so writers as for Clement of Rome (quasi-legendary!), Papias and Polycarp) were called bishops, either posthumously or in their latter years.
Could Ignatius have been the bishop of Antioch?
Hardly so, considering:
a) As explained above, true bishop did not exist during Trajan's reign (even years after) or before.
b) The first three letters present him as a lesser member of a church somewhere in Syria.
c) Only one letter, the fourth one, mentions Ignatius as the bishop from Syria, in passing, without specifying the city and for obvious glorifying reasons.
d) Corroborating external evidence for Ignatius as bishop appears as late as some one to two centuries later (Origen & Eusebius), by two authors who did not agree about Ignatius' predecessor as bishop of Antioch!

In the Ignatian letters, we see the situation as it was in a few cities in Asia minor, around 135: struggling church leaders, sometimes with close associates, who needed all the help they could get in order to expand and/or solidify their position. But how?
a) By having a martyr (in transit!) praising the merit of an unified city-wide church under the complete control of a bishop; with the later word for the first time being promoted to a new meaning: overseer, not only of some believers with possibly also a few deacons, but of the whole city-based Christian community, including all clerics & lay persons:
"... submitting yourselves to your bishop and presbytery, you may be sanctified in all things." (Ephes.2.2)
"... your revered bishop, and with the fitly wreathed spiritual circlet of your presbytery, and with the deacons who walk after God. Be obedient to the bishop ..." (Magn.13:1-2)
And Christians on the outside were not acceptable:
"I congratulate you who are closely joined with him [the bishop] as the Church is with Jesus Christ ... that all things may be harmonious in unity." (Ephes.5:1)
"Whosoever therefore comes not to the congregation, he does thereby show his pride and has separated himself ..." (Ephes.5:3)
"... Assemble yourselves together in common, every one of you severally, man by man, in grace, in one faith and one Jesus Christ ..." (Ephes.20:2)
"... some persons have the bishop's name on their lips, but in everything act apart from him. Such men appear to me not to keep a good conscience, forasmuch as they do not assemble themselves together lawfully ..." (Magn.4:1)
"Hasten to come together all of you ..." (Magn.7:2)
"And attempt not to think anything right for yourselves apart from others: but let there be one prayer in common, one supplication, one mind ..." (Magn.7:1)
"... Let no man do anything pertaining to the Church apart from the bishop ..." (Smyrn.8:1)
"... he that does anything without the knowledge of the bishop renders service to the devil." (Smyrn.9:1)
b) By presenting themselves as blessed by the glorious martyr, after they allegedly met with him, at a time when they were "silent" (Ephes.6:1, Philad.1:1) or "young" (Magn.3:1), long before the epistles were written (when the prophesied (allegedly!) troubles happened --Trall.8:1, Smyrn.4:1--).
c) By laying out, through the authority of the godly martyr, what the local flock should believe (their own orthodoxy) and what should be rejected (heresies, Gnosticism, Judaism).

Who would be the authors of each of these epistles?
Probably the struggling proto-bishop himself, or anyone among his close associates/confidents or even any lay Christian wishing for (an "Ignatian") unity in his city. By the time the letters were written, some of the alleged named visitors of Ignatius might have passed away, therefore unable to offer (possibly unfavorable!) testimonies.

Let's note each meeting (with very few) in the first three letters occurs when Ignatius is in Smyrna, and NOT in the city of his visitor(s). That would make more difficult for a local dissenter to claim the meeting never took place (or Ignatius was not in the area). And the NO reading (or reading) of a particular letter several decades ago is unlikely to be remembered. Also, the letter could be claimed to be lost & found.

'To the Ephesians':
This letter (the longest of the lot) was the one which started the series. But its writer had no idea others would used it as a template for their own community. Instead, the author, definitively a Christian from Ephesus, had another plan in mind, that is to write another epistle to the same, but apparently that did not get done:
"... in my second tract, which I intend to write to you, I will further set before you the dispensation whereof I have begun to speak, relating to the new man Jesus Christ ..." (20:1)
The author is very likely among those three, by order of probability:
1) "... I have received your whole multitude [the Christians of Ephesus] in the person of Onesimus, whose love passes utterance and who is moreover your bishop -- and I pray that you may love him according to Jesus Christ and that you all may be like him; for blessed is He [God] that granted unto you according to your deserving to have such a bishop." (1:3)
"For if I in a short time had such converse with your bishop, which was not after the manner of men but in the Spirit how much more do I congratulate you who are closely joined with him as the Church is with Jesus Christ and as Jesus Christ is with the Father, that all things may be harmonious in unity ... For, if the prayer of one and another has so great force, how much more that of the bishop and of the whole Church." (5:1-2)
2) "... my fellow-servant Burrhus, who by the will of God is your deacon blessed in all things ..." (2:1)
3) "... Crocus also, who is worthy of God and of you ..." (2:1)

The Ephesian emerging "Catholic" church was under siege then by (vaguely defined!) "heretics", possibly disapproved presbyters:
"For some are wont of malicious guile to hawk about the Name, while they do certain other things unworthy of God. These men you ought to shun, as wild-beasts; for they are mad dogs, biting by stealth; against whom you ought to be on your guard, for they are hard to heal." (7:1)
"... a man through evil doctrine corrupt the faith of God for which Jesus Christ was crucified. Such a man, having defiled himself, shall go into the unquenchable fire ..." (16:2)

'To the Magnesians':
The four named ones here would be the most suspect regarding the authorship:
"I was permitted to see you in the person of Damas your godly bishop and your worthy presbyters Bassus and Apollonius and my fellow-servant the deacon Zotion, of whom I would fain [gladly] have joy, for that he is subject to the bishop" (2:1)

Note: let's notice Zotion is congratulated for being directly under the bishop. It seems here a three levels hierarchy is not wished for, but one with only two: bishop, then below presbyters & deacons. Presbyters appear to be the bishop's own men, some inner court, while the deacons would be self-appointed ministers to the faithful. And generally speaking, in the Ignatian letters, the diaconate is more important than the presbytery, and closer to the people than the bishop & his circle of presbyters:
"... For your honourable presbytery, which is worthy of God, is attuned to the bishop ..." (Ephes.4:1)
"... the bishop presiding after the likeness of God and the presbyters after the likeness of the council of the Apostles, with the deacons also who are most dear to me, having been entrusted with the diaconate of Jesus Christ ..." (Magn.6:1)
"... deacons of the mysteries of Jesus Christ must please all men in all ways ..." (Trall.2:3)
"let all men respect the deacons as Jesus Christ ... the bishop as being a type of the Father and the presbyters as the council of God and as the college of Apostles ..." (Trall.3:1)
"... the bishop and the presbyters who are with him, and with the deacons that have been appointed according to the mind of Jesus Christ ..." (Philad.0:0)

The main foe of this congregation was Judaism:
"Be not seduced by strange doctrines nor by antiquated fables, which are profitless. For if even unto this day we live after the manner of Judaism, we avow that we have not received grace:" (8:1)
"It is monstrous to talk of Jesus Christ and to practise Judaism. For Christianity did not believe in Judaism, but Judaism in Christianity ..." (10:3)

'To the Trallians':
Here, Polybius is the only alleged visitor from Tralles, and most likely the author, considering:
a) "... your bishop [Polybius], whose very demeanour is a great lesson, while his gentleness is power -- a man to whom I think even the godless pay reverence. Seeing that I love you I thus spare you, though I might write more sharply on his behalf: ..." (3:2-3)
b) "Am I not able to write to you of heavenly things? But I fear lest I should cause you harm being babes. So bear with me, lest not being able to take them in, you should be choked. For I myself also, albeit I am in bonds and can comprehend heavenly things and the arrays of the angels and the musterings of the principalities, things visible and things invisible ..." (5:1-2)
As I explained before, it is most inconceivable Ignatius would be challenged (by Polybius, very unlikely!). Therefore it is quasi-certain Polybius was trying to answer his critics, among them Basilidian Gnostics who had a very developed concept of heavens, angels & principalities (as shown already in "Time of writing").

Note: it is also in this epistle that Ignatius foresees future troubles, not existing yet during his days.

'To the Philadelphians':
The bishop, despite his silent behavior, is described in the best terms:
"... And I am amazed at his forbearance [of the unnamed bishop]; whose silence is more powerful than others' speech. For he is attuned in harmony with the commandments, as a lyre with its strings [hard to notice if he is quiet!]. Wherefore my soul blesses his godly mind, for I have found that it is virtuous and perfect -- even the imperturbable and calm temper which he has, while living in all godly forbearance." (1:1-2)
There is a good chance this bishop wrote the letter even if he did not name himself.
And Judaism was a problem here also:
"But if any one propound Judaism unto you, hear him not: for it is better to hear Christianity from a man who is circumcised than Judaism from one uncircumcised. But if either the one or the other speak not concerning Jesus Christ, I look on them as tombstones and graves of the dead ..." (6:1)
It seems some non-Jew preachers were propounding Judaism to Christians! And without mentioning Jesus Christ!
The Christian community was very divided:
"... But assemble yourselves all together with undivided heart." (6:2)
"... I cried out, when I was among you; ... Give you heed to the bishop ... Howbeit there were those who suspected me of saying this, because I knew beforehand of the division of certain persons. But He in whom I am bound is my witness that I learned it not from flesh of man; it was the preaching of the Spirit who spoke on this wise;
[that seems to be a pre-emptive measure against those who might think this bishop cued Ignatius about what to say, then or now!]
` ... Do nothing without the bishop; ... cherish union; shun divisions ..." (7:1-2)

How to explain 'to the Philadelphians' states Ignatius spoke to the community, if it was not true?
Local believers in the area would be already used to 'glorious Ignatius in Asia', through the other letters. Furthermore, 'to the Romans' says Ignatius travelled "by land and sea" (5:1) and Philadelphia is inland between Smyrna & Syria. So the possibility was there ... And some thirty years later, it would be difficult for anyone to claim this meeting did not take place. More so because, since that time, most local Christians either died, moved away or denied their faith. The remaining elders were not likely to object, certainly not the bishop with his presbyters & deacons.
And the believers then were deemed to accept the epistle was written long ago, although never heard of before (as also for GMatthew, GLuke, 'Acts', 'Ephesians', '2Thessalonians', the "Pastorals", '2Peter' & many 2nd/3rd cent. uncanonical writings in the name of Jesus' contemporaries). So the same ones would be expected to accept the meeting occurred in the past, in their own city, even without any prior knowledge of it.
Of course, Ignatius addressing the whole community is more potent than private meetings in Smyrna (probably doubted by then or too much "déjà vu"!).
Did that work? Maybe not, because the next epistle does not state any community meeting with Ignatius when allegedly in Smyrna ...

'To the Smyrnaeans':
Here the bishop is unnamed and without characteristics (and no local presbyters or deacons mentioned by name either). But the authorship might very well come from one of these lay persons:
"I salute the household of Gavia, and I pray that she may be grounded in faith and love both of flesh and of spirit. I salute Alce, a name very dear to me, and Daphnus the incomparable, and Eutecnus, and all by name ..." (13:2)

Who was Ignatius?
Considering:
a) The incongruities of (& for) Ignatius' trip from Syria to Italy
b) Ignatius presented initially as just a member of a church in Syria and suffering execution in Rome
c) Ignatius' martyrdom, with the prestige derived from it, being used (aggressively) from the first letter
d) The sevens letters of the middle recension being written many years after the alleged facts, by Asia minor Christians for their own benefit and/or church
It is most likely:
Ignatius was truly a zealous Christian from Syria who got executed in Rome (likely for his preaching), probably during Trajan's rule. However the offence was not committed in Syria, but in Rome.
Then, later on, Ignatius' city of origin got forgotten as also the place of his condemnation. And because he was still fondly remembered as a Christian from Syria given to the beasts in Rome, a preeminent cleric of Ephesus postulated his "crime" occurred in Syria, forcing the already convicted martyr to travel westward, through Asia minor (as a detour!), and, above all, on his way, addressing the Ephesians after he "received your whole multitude in the person of Onesimus, ... who is moreover your bishop" (Ephes.1:3)
And if the letter helped Onesimus to assert his authority as THE bishop of Ephesus, then, in another city not too far away ...

PS: despite all the inconsistencies in Ignatius' story and epistles, the majority of contemporary scholars follows the conclusion of "researches" made by Zahn (1873) & Harnack (1878), both protestant scholar, and Lightfoot (1885,1889), an Anglican bishop; that is the middle recension seven epistles are authentic. And Harnack, the eminent German theologian, tried to close the door behind him: "whoever considers the Ignatian letters to be spurious, has not studied them thoroughly", explaining why these aforementioned outdated "studies" received little criticism and continue to rule.