When parents of a child were never married, Oklahoma law places custody of the child automatically with the biological mother, even if the father signed an acknowledgement of paternity, and even if the father is named on the child's birth certificate.

The father's only right to the child is his duty to pay child support.

In these circumstances, the father would typically benefit significantly by initiating a lawsuit to obtain an order to judicially establish his parental rights, including his custodial rights and rights to visitation. 

The father will not have legal rights, and the mother retains all custodial rights and control, unless the father files and gets a judicial order that expressly determines that he is the father and that he has parental rights of custody and visitation.

Same-sex couples have similar rights and obligations. 

Oklahoma law provides for a 2 year "lookback" in these cases for child support. When an individual is determined to be the father, the judge is required to order the father to pay past-due child support for the two years prior to the filing of the petition initiating the case.