This is a request she is making, what you need to do is defend against it. It is possible? It can be unless you demonstrate to the court that you should not be punished for the willful acts of the mother, such as lying about your paternity, her sitting on her rights and not asking to establish paternity sooner and wait until such a long time has gone by.
I agree a lawyer is needed to contest their requests, since there is some history here that she is to blame for all this time wasted and the misrepresentation she has commited that should be heard by the court.
If you are court ordered and you violate the court orders the Judge has the discretion to sanction you for the violations and place you in jail for five days. If you mean go to jail for not paying the child support, it is possible but that will depend on whether you have intentionally and willfully failed to pay as court ordered.
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