I am not in a relationship with my child's father and never have been, but we have contact and he sees her from time to time, does he have any parental rights to her if he has not signed the birth certificate?

He does, he just has to go to court to enforce them. The judge could order a paternity test first. He has both parental rights and responsibilities. Have you asked for child support yet?

Merely not being on the birth certificate does not take away his rights, only requires him to prove paternity to get them.

He may at anytime file for joint custody, visititation, and other rights as he desires. It will be up to the court to decide what level he will get.

You of course should have filed for child support once the child was born.