In 1 Timothy 1:2, The King James Version says “to Timothy, my OWN son in the faith.” The Greek word is γνησίῳ. Other translations render this word as follows:
ESV, NIV, NASB, CSB, NAB- true
ISV, NET – genuine
NRSV- loyal
I think this means “true son” in the sense of 2 Cor. 5:16, “Therefore from now on we know no man after the flesh” and Matt. 12:50, “For whoever does the will of my Father in heaven, that person is my brother
and sister and mother.”