We don't know when St. Peter was bishop of Rome, but his first letter hints at his being located there (1 Peter 5:13), and of course that is what has been traditionally believed. St. Peter also consecrated the bishopric of Antioch:
The most famous scriptural reference concerning Antioch relates that it was in this city that the followers of Christ were first mockingly referred to as "Christians" (Acts 11:26). In the Book of Acts, which offers an account of the first years of the Church, we discover that Antioch is the second most frequently mentioned city. Nicholas, one of the original seven deacons was a convert from Antioch and perhaps the first Christian from that city (Acts 6:5). During the persecution which occasioned the death of Saint Stephen the First Martyr, members of the fledgling Christian community in Jerusalem fled to Antioch for refuge. Church tradition maintains that the See of Antioch was founded by Saint Peter the Apostle in A.D. 34 . Peter was either followed or joined by the Apostles Paul and Barnabas who preached there to both Gentiles and to Jews, who seem to have been numerous in the city. It was in Antioch that one of the first conflicts within the Church developed between Peter and Paul. This conflict regarded the necessity of circumcision for male Gentile converts to Christianity. It was the resolution of this conflict at the Council of Jerusalem under Saint James the Apostle that determined the direction of the Antiochian mission to the Gentiles, and the dynamic nature of that Christian community in its missionary outreach. It was from Antioch that Paul and Barnabas departed for their great missionary journeys to the Gentile lands (Acts 13:1).
Founded by Saints Peter and Paul
We don't know when St. Peter was bishop of Rome, but his first letter hints at his being located there (1 Peter 5:13), and of course that is what has been traditionally believed. Thank you for your honesty. I think he was probably there at some time, but never really as a bishop. If that were so there would have been some kind of record.
As soon as you start referring to "tradition" I skip the rest. No offense intended, but I could say it is a Baptist tradition that we were the church that baptized Jesus. It was John the Baptist after all and it is tradition. Doesn't make it true, does it?