McCree, you wrote and quoted from " Eusebius " but you left out the following by Eusebius.
' 'You have thus by such an admonition bound together the plantings of Peter and Paul at Rome and Corinth." Dionysius of Corinth, Epistle to Pope Soter, fragment in Eusebius' Church History, II:25 (c. A.D. 178).
"As Peter had preached the Word publicly at Rome, and declared the Gospel by the Spirit, many who were present requested that Mark, who had followed him for a long time and remembered his sayings, should write them out." Clement of Alexandria, fragment in Eusebius Church History, VI:14,6 (A.D. 190)
"It is, therefore, recorded that Paul was beheaded in Rome itself, and that Peter likewise was crucified under Nero. This account of Peter and Paul is substantiated by the fact that their names are preserved in the cemeteries 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. 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 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.'" Gaius, fragment in Eusebius' Church History, 2:25 (A.D. 198).
"Peter...coming to the city of Rome, by the mighty cooperation of that power which was lying in wait there..." Eusebius, Ecclesiastical History, II:14,5 (A.D. 325).
"This man [Simon Magus], after he had been cast out by the Apostles, came to Rome...Peter and Paul, a noble pair, chief rulers of the Church, arrived and set the error right...For Peter was there, who carrieth the keys of heaven..." Cyril of Jerusalem, Catechetical Lectures