Peter identifies him as his son.
It would appear that just as Paul had spiritual sons (Timothy, 1 Timothy 1:2; 2 Timothy 1:2; and Titus, Titus 1:3), so Peter had a spiritual son. It is striking that after the angel freed Peter from prison he went directly to the house of Mary, the mother of … Mark,
where he was so well known that the servant girl immediately recognized his voice (Acts 12:12–14). Scripture provides us with more details about Mark’s cooperation with Paul (see Acts 12:25; Colossians 4:10; 2 Timothy 4:11; Philemon 1:24) but is silent about his further relation with Peter. Yet the church fathers tell us that Peter and Mark worked closely together to the point that some would suggest that Mark’s Gospel reflects Peter’s recollection of Jesus’ earthly ministry. That Mark also sends greetings is intended as further encouragement for the beleaguered saints of the Dispersion inasmuch as Mark joins in prayer for God’s peace upon them. He, after all, as Peter’s son,
is like-minded to his spiritual father.
13 She who is at Babylon, who is likewise chosen, sends you greetings, and so does Mark, my son.