A.T. Robertson Commentary Titus 1:4

"to Titus, my true child after a common faith: Grace and peace from God the Father and Christ Jesus our Saviour." — Titus 1:4 (ASV)

My true child (γνησιω τεκνω). See 1 Timothy 1:2 for this adjective with Timothy. Titus is not mentioned in Acts, possibly because he is Luke's brother. But one can get a clear picture of him by turning to 2 Corinthians 2:13; 7:6-15; 8:6-24; 12:16-18; Galatians 2:1–3; Titus 1:4f.; 3:12; 2 Timothy 4:10. He had succeeded in Corinth where Timothy had failed. Paul had left him in Crete as superintendent of the work there. Now he writes him from Nicopolis (Titus 3:12).

After a common faith (κατα κοινην πιστιν). Here κατα does mean standard, not aim, but it is a faith (πιστιν) common to a Gentile (a Greek) like Titus as well as to a Jew like Paul and so common to all races and classes (Jude 1:3). Κοινος does not here have the notion of unclean as in Ac 10:14; 11:8.