If everyone is in agreement, you can get DNA testing done at Physician's Services or ArcPoint here in Cleveland. Otherwise, the only way to get a test done is through a court action or petition. You could not do this for you are not a party to the lawsuit. Only the mother or father can bring the lawsuit. Without doing any research, there may be a possibility that an individual could bring an action against mom or dad on behalf of the child as "next of friend".
Hope this helps.