Child Custody

Legally, signing a birth certificate as the "father" (according to blacks law definition) gives legal right to collect income support, etc from the father. In a situation where the biological father has not signed a birth certificate and has not established paternity in New Jersey. What rights as a "Man" does he have in order to gain some kind of custody for his offspring?, if the mother has signed the birth certificate, but wont allow the father to see the offspring?   Please note the definition of "Father" in  this question is not be related tot he definition on "FATHER" in the Black law dictionary?