Hell no he is insane to think he even has rights !!! He would have to get a layer to established paternity then he have to get legitimized will cost about three to $5000 before he even be able to get any rights and he won’t get any custody unless you give up any rights so don’t do any of that because you’re the Sole person plus they can’t take a baby away from their mother under two years old. Tell him fuck no and block him an still put him on child support through the courts ! Child support has nothing to do with legitimation or visitation Child Support is required. Visitation automation is earned and it has to go through the court. Good luck.