You should consider bringing a suit to terminate the father's parental rights. Under the Texas Family Code, to terminate the parent-child relationship, the court must find clear and convincing evidence (this is higher than other levels involved in family law cases) supporting at least one of 25 grounds for termination set forth in Chapter 161 of the Texas Family Code.
The 25 statutory grounds can generally be broken up into five broad categories: (1) the parent consents to termination; (2) the parent abandons or does not support the child; (3) the parent endangers the child; (4) the parent engages in criminal conduct; and (5) the parent is otherwise proved to be unfit.
Based on the limited facts you stated, one possible ground applicable to your situation is that the father abandoned the child and did not pay child support. What is unclear from your facts is how long the father has not paid child support for your son. In order to use this ground as a basis for termination, the father has to have not paid child support for at least one year.
I hope this helps. My firm has defended and prosecuted termination of parental rights cases in Dallas, Collin, Tarrant and Denton Counties.Ask a similar question