I was wondering how you might go about having the other parent Relinquish his rights to a child he wants nothing to do with but the state is making me open a child support case or lose my Medicaide.

You can't, unless you get married, and have a new partner that will adopt And if he wants nothing to do with that child he will just not use any of his rights.

Why do you think it is fair for me and other people to pay our tax money for your medicaid if you are not willing to make the father pay his legal duty.
I get on a real high horse on this type of thing, that is not FREE money, someone is paying it, and the first persn should be the father