Texas has a presumed limitation on the amount of back support to be paid -- it is presumed that 4 years of support is in the best interest of the child unless the mother can prove (1) the father knew or should have known he was the father of the child and (2) "sought to avoid the establishment of a support obligation. " Tex. Fam. Code sec. 154.131(d). Child support is calculated based on his income. It sounds like he needs a Texas lawyer to protect him and put together the paperwork. Look here in Avvo for a lawyer in the county where the case is filed who handles child support cases. Good luck to both of you.
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Child support and visitation are two separate issues. So child support is enforceable even if the parent denies access to the child. The reverse is also true, even though he doesn't pay she isn't permitted to withhold the child. Sounds like you all need to go back to court.