Father is on Birth cert and Has paid child support since birth. Child living w/dad for over a year. already abated support order

Mother left son With Dad over a year ago. sees him at least once weekly. Father has paid child support since birth and is on birth certificate. Father looking to gain Legal custody due to the nature of the the mother. Father has already filed and been granted abatement of Support. Does dad need to file a petition to be recognized as the father at this point? Can She take him if she got a wild hair? What is Fathers First step?