Does the father, my ex common law husband, have to pay 1/2 or anything towards the prenatal care of our unborn child? Medical bills, copays, prescriptions? He claims he doesn't. I don't know.

You will probably have to check with a lawyer.

Depending on the laws of your state, he may or may not be liable for those bills.

The question is: Why is he denying care to his unborn child?

Nope. He has to contribute to the child's financial support once born but doesn't have to pay a dime before then.