If the mother won’t sign an affidavit acknowledging you as the biological father then you can take legal action to establish paternity (eg a court ordered DNA test).

But the court would not likely give you joint or shared custody when you have no ongoing relationship with the mother and clearly have no non-biological relationship with the mother (mayyyybe you could get some visitation?).

But the court won’t order her to let you touch her belly, and a court won’t order you two back together.

And since you don’t have money for a legal consult you obviously don’t have money for child support so I don’t think you know what you want here.