Being asked to pay child supp of a child born out of my marriage. Not sure if mine besides I want nothing to do with the child never signed birth cert

Your first step would be requesting a paternity test to determine if you are the biological dad. If you are, then the court will order that you pay child support to the mom based on your income. This is true whether or not you wish to ignore the child.  You may also be ordered to provide health insurance for the child or to pay the mother for the cost of health insurance she provides.   Courts will terminate a parent's rights to a child if the court determines that is in the child's best interest. The courts do not normally determine it is in the child's best interest to terminate the rights of a parent because having two parents supporting a child makes it more likely that  the child will not require state aid to survive, than if only mom has to support the child.  In addition the court does not want to create a situation where the mother needs to seek state aid in order to survive as a single parnt, which is likely to happen if your rights were terminated.   The short answer is that most courts are not going to terminate your rights unless the mother agrees and even then, the courts usually prefer to have a new parent being established-- a step-parent adopting the child-- in order for the termination of the biological dad to be approved.