Other than Eusebius and Jerome, and they were late, in the 4th century, I have found no other early church patriarchs that give credence to Peter's Bishopric.
I checked Clement of Rome, Ignatius, Justin Martur, all of whom were early enough and connected enough to Rome to know the facts. If anyone would attest to his Bishopric, they would, but there is nothing in their writings. Surely Peter's Bishopric in Rome would show up in their writings if he had been there, right?
The earliest attestation that Peter was even in Rome was Irenaeus whose only attestation is of the "Church founded and organized at Rome by the two most glorious Apostles, Peter and Paul". That's all. There is no mention of a 25 year bishopric, Nero, dates, crucifixion, or death of Peter in Rome.
Where did Irenaeus get his information that Peter had been in Rome with Paul establishing the Church there if it is not in Scripture or in any of the patriarchal writings before him? Did he just make it up or did he read about in the Gnostic Clementine literature that was going around which was hardly credible?
What credible patriarchs of the early Church am I missing?
You seem to forget that Irenaeus was a pupil of Polycarp, who was an auditor of the Apostle John. You live in a society and culture in which something must be written down for it to have credibility. You are seemingly imposing that notion on a time and culture in which many things were passed down orally.
Irenaeus is a very trustworthy source, both in his character and given the fact that he spent considerable time in Rome as an envoy (if I remember correctly). Dionysius, bishop of Corinth (c. 166-174 AD), also writes that both Peter and Paul planted both in Rome and in Corinth, and suffered martyrdom at the same time. And there is no competing traditional account of Peter's life. Peter himself gives evidence of his being in Rome in 1 Peter 5:13. And Papias (bishop of Hieropolis) and Clement of Alexandria both testify that Mark wrote his Gospel at Rome, which Gospel is understood to have been written under the direction and authority of Peter. (See, for example, 1 Pet 5:13) This Clement of Alexandria (c. 150 - 215 AD) also tells us that Peter preached at Rome. Tertullian also refers to "those whom Peter baptized in the Tiber", and tells us that Clement (of Rome) was ordained by Peter at Rome. Remember too that unlike in the case of Paul, there is no evidence of Peter being brought to Rome to stand trial. Nor would Peter, not being a Roman citizen have needed to be brought to Rome to face Nero or to be executed. But there is much evidence that Peter was martyred in Rome. The best explanation of those three facts is that Peter was already in Rome, on his own accord. And there is long-standing and undisputed tradition that Peter went there early, in part to deal with the false teaching of Simon Magus (who apparently had gone to Rome and through his sorcery become so revered that had a statue of himself as a god set up in Rome). St. Cyril (bishop of Jerusalem) testifies to that, and there are other sources for that as well.
-A8