Legal Question in Family Law in California

It depends. The birth certificate is of no legal significance. However, for at least the last ten years a father's name has not been supposed to go on the birth certificate unless he was the husband of the mother or both the mother and father signed a voluntary declaration of paternity. That declaration has nearly the same power as a judgment of paternity. Presumably you and the mother signed one of those declarations, or you should not be on the birth certificate. If that is correct, then you are the legal father and have the full legal rights of a father. Only if another man who is the actual biological father comes forward and contests your paternity could you lose your paternal rights (and responsibilities, i.e., child support). Otherwise you are the legal father of the child the same as if you had adopted him or her, or were the biological father.