How can I get my child's father name off the birth certificate?

BC is not the way to attack this problem. It might be possible to get his rights terminated but not on these facts. Do you have a step-parent ready to adopt? Courts generally won't leave a child without a father. Also, you cannot seek support and termination at the same time. Termination relieves the obligation of support. You really need an attorney to help you with this. It might be possible for you to get restricted/ supervised visitation.

I'm assuming he lives in Dallas or Fort Worth and hasn't moved to Mexico yet. I'm also assuming this is a child support case that you filed through the Attorney Generals Office. If so, does the child live primarily with you or father?

You can get his name off the birth certificate if and when legally he is not your child's father, meaning his parental rights have been terminated or you obtain some court order that he is not your child's father.. Otherwise his name remains on the birth certificate. Texas law presumes it in a child's best interests for parents to be appointed joint managing conservators with one parent designating primary residence without regard to geographical location or within some geographical area. Visitation will be based on your child's best interests. Once court orders are in place he would be committing a felony if he were to take your child from you contrary to court orders. Your fear is a common fear, but once court orders are in place your fears should diminish. You should try to get family law counsel to protect yours and your child's interests as the Attorney General represents the State of Texas.

The only way to get his name taken off of the birth certificate is to terminate his rights. As long as he is found to be the child's biological father, his name will be recognized and remain on the birth certificate. If you terminate his rights, you understand that he will no obligation to pay you child support.