"It Wasn't His Child" was written by Donald R. Ewing II. Trisha Yearwood did the best-known recording of it.
I think Kenny Rogers also recorded this song.   At least I know I've heard a male country artist sing this song.

I posted the lyrics and songwriter credits in this thread:
Lyr. Add: "It Wasn't His Child (Christmas)"   

along with links to some videos of the song