giving up parental rights

My husband is being accused of being the father of a 1yrs old girl. which he had never seen nor DNA test been done to prove that. Her mother calls him about every 3-4months to harasse him. She tells him that she will file for child support and them tells him she just has not done so. she wants to wait a few years so he has to pay intrest. He has never seen the child never was married to that women. If the child ends up being his can he give up his parental rights and not pay child support? if it help any we live in Texas.

i know that (at least in michigan) if you sign over parental rights, you cannot waive child support, unless she doesnt go after it. on the other hand if another man adopts the child it would waive child support.