The next court that would hear an appeal from the State appellate court would be the the state supreme court.
When a state trial heads to a court, it first goes to the State trial courts. If a disagreement is made then it would go the the state appellate court to hear the appeal. Then, it would head to the State supreme court if another appeal is made. Which then would head the the U.S. Supreme Court where both state and federal requests are reviewed.
