“I went to probate court to determine the amount of child support and while there I asked the judge about paternity test and I was denied paternity test because the judge did not want to basturize the child. Can a judge deny a paternity test when my name is not on the birth certificate?”

The law in every state is different as to at what point in time someone can challenge paternity. In many states the statutes of limitation are quite short. In some it has to do with when the putative father first learned that he might not in fact be the biological father. In addition, the laws in many states are evolving and changing rapidly. You should consult a qualified family law attorney in your state as soon as possible.