Go to the OAG. Ask the OAG to get you child support from the child's father. The OAG can file a suit affecting the parent-child relationship to determine paternity and to set child support. This will get done what you want to accomplish.
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
The Attorney General's office can file a suit to establish him as the father. They can do a DNA test and it won't cost you anything.
I am licensed to practice law in the great state of Texas only. The above answer does not create an attorney/client relationship. These responses should be considered general legal education and are intended to provide general information about the question asked. Frequently, the question does not include important facts that, if known, could significantly change the answer. Information provided on this site should not be used as a substitute for competent legal advice from a licensed attorney that practices in your state. The law changes frequently and varies from state to state. You should verify and confirm any information provided with an attorney licensed in your state.
Sign up to receive a 5-part series of useful information and advice about child custody law.