No. You cannot voluntarily terminate your obligation to pay support to a child. The only way to do this is if another adult (generally, the spouse of the other parent) agrees to adopt the child and assume that responsibility.
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First of all, it is no one's business regarding how the child is supported and raised unless it comes into the attention of the government. So, unless CPS is involved or there is a court proceeding, you can raise your child the way you want to raise it, with or without child support.
In Texas, most courts will not order child support obligation on someone who is not been confirmed as the father of the child unless the "father" voluntarily takes on that responsibility. Once the "father" volunteers, then all bets are off. Even if the "father" is not the real father, it is still up to the court to decide whether that child support needs to continue or not. A lawyer would be a great idea right now while it is still cheap. Once it becomes a hotly disputed court fight, it would be too late for any "I should have".