There is no documented history, contemporary with Peter, that can prove he even ministered in Rome. We do know however, without a doubt, that Paul ministered there for at least two full years (Acts 28:30). And it was he, not Peter, who wrote the doctrinal Epistle to the Romans. A literary form of “feeding” them.
Here are more genuine historical writings attesting to the fact that Peter was indeed in Rome.
St. Irenaeus, “Against Heresies”, 3,1,1, 180 A.D., J208
“…in their own dialect, while Peter and Paul were evangelizing at Rome, and laying the foundation of the church.”
St. Irenaeus, “Against Heresies”, chapter lll,
“…the very ancient, and universally known Church founded and organized at Rome by the most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops.”
Tertullian, “The demurrer against the heretics”, chapter XXXll,l,
“… like the church of the Romans where Clement was ordained by Peter.”
St. Peter of Alexandria, “The Canonical Letter”, canon 9, 306 A.D.
“Peter, the first chosen of the Apostles, having been apprehended often and thrown into prison and treated with ignomity, at last was crucifired in Rome.”
Eusebius,“The Chronicle” Ad An, Dom 68, J651 cc
“Nero is the first, in addition to all his other crimes, to make a persecution against the christians, in which Peter and Paul died gloriously in Rome.”
Eusebius, “History of the Church”, 3,2, 300 A.D., J652a
“After the martyrdom of Paul and Peter, Linus was the first appointed to the Episcopacy of the Church at Rome.”
St. Damasus I, “The Decree of Damasus” 3, 382 A.D., J910u
“The first see, therefore, is that of Peter the Apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it.”
As to the common controversy with regard to l Peter 5: 13 that the word Babylon there does not refer to Rome, here is a quotation from a n-catholic author;
“The City of Babylon - It remained an important city through the Persian period. Alexander the Great would have restored its glory, but his plans were cut short by death. After him it declined. By the time of Christ its political and commercial supremacy had gone. For centuries it has been a desolate heap of mounds, a place for the beasts of the desert; a remarkable fulfillment of prophecy: (Isa. 13: 17-22) (Jer. 51: 37-43).”
Halley’s Bible Handbook pp. 338 - 339 24th edition