Father is signed exactly like daddy, if you are referring to a biological, foster, adoptive, or stepfather: make the number 5 sign in ASL, then tap the thumb end on your forehead. Another trick to help you remember father is that male signs are always above the nose, and female signs are below the nose - so the sign for father is the same as the sign for mother, just a little higher.
However, if by Father you mean a spiritual father, priest, or minister, then take your letter G hand and run the index finger and thumb a short distance across the front of your neck just under your chin, signifying the priestly or ministerial white collar.
If you are or your spouse is the father of the family, you can wait till you or he catches your baby's attention, then say to your baby, "Father," and do the sign. You or he can also introduce yourself/himself to your baby upon entering the room. Lastly, to give your baby a sign of continuity, you can also introduce your or your father's spouse as your father, or your baby's grandfather.
Stick a picture of your baby's father over this stock photo. You don’t want your baby growing up thinking that their father is this guy, or maybe you do. In any case, we will not be responsible for the years of therapy!