James ,again ,welcome to the forum. Sorry to hear of your loss ,no matter how long ago it was.
Your fathers Combat Magnum was one of the first 1000 produced and probably shipped in 1956.
Remove the stocks (grips) carefully ,,and the actual ser.# will be on the bottom of the grip frame.
It's touching to hear of how you shot the revolver with your pop when you were a kid. I have no such memories ,but would like some good ones like that
.
Others will add info. as this goes on , one thing for sure ,,that gun sure is a beauty!
Page 136 in the 3rd. ed. of S.c.S.W. has the info on the first K Frame 357s.
Regards ,AL