Again, in the same books, Clement gives the tradition of the earliest presbyters, as to the order of the Gospels, in the following manner: The Gospels containing the genealogies, he says, were written first. The Gospel according to Mark had this occasion. 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. And having composed the Gospel he gave it to those who had requested it. When Peter learned of this, he neither directly forbade nor encouraged it. But, last of all, John, perceiving that the external facts had been made plain in the Gospel, being urged by his friends, and inspired by the Spirit, composed a spiritual Gospel. This is the account of Clement.
'Marcus, my son, saluteth you' [ 1 Pet 5: 1 3 ] . Mark, the follower of Peter, while Peter publicly preached the Gospel at Rome before some of Caesar's equites, and adduced many testimonies to Christ, in order that thereby they might be able to commit to memory what was spoken by Peter, wrote entirely what is called the Gospel according to Mark.'
They say, accordingly, that the blessed Peter, on seeing his wife led to death, rejoiced on account of her call and conveyance home, and called very encouragingly and comfortingly, addressing her by name, 'Remember thou the Lord.' Such was the marriage of the blessed, and their perfect disposition towards those dearest to them.
Clement of Alexandria (c. 150-215 A.D.), via Eusebius