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Have you had a meeting with the Office of the Attorney General yet, or where you just served papers?
If she has refiled to ask for support again, your defense would be that you care for the child the majority of the time. The OAG cannot give you legal custody of your child, so if you want to get legal custody of your child on paper, you will need to ask a Judge to give you custody on paper. You would do this by filing a Suit Affecting the Parent Child Relationship (SAPCR), and you can find the forms on www.texaslawhelp.org.
All the OAG does is decide who pays child support. You could counter-file on her asking her to pay child support since it sounds like you actually have primary custody.