Legal Question in Family Law in Texas

You've asked two questions:

1. Can he fight for custody? Yes, but if by custody you mean he takes the child from its mother, he will have to prove by clear and convincing evidence that the child's circumstances are such that the child would be better off with him.

2. Can you adopt the baby? Yes, the mother can sign an affidavit of voluntary relinquishment of parental rights and you can ask the court to allow you to adopt the child.