Father is stating that birth mother never told him she was preagnet , and that when he asked her if she was she said no. father never registered and now after three months of my wife and I having the baby with us .The fatherhas come back into play saying he just found out about the baby and wants her back. Does he have any rights to the baby in New York state.

Yes, unless it can be proved that the birth father knew about it. Are you and your wife adoptive parents ?
If so your attorney should have tried to contact the father.

If he's the legal father, yes, he has rights.

What is your relationship to the child and, as my colleagues said, was this a legal adoption? Foster care? Guardianship? No paperwork at all?