On the TV show "Law & Order", when they cut to the trial it's usually accompanied by a chiron (along with the trademark "dun-dun" sound) saying something like "New York State Supreme Court, Part 7". Is this an accurate representation of where trials like these would be held? Isn't the NY Supreme Court an appeals court, like SCOTUS? These are always ordinary jury trials. (Considering the contorted logic the prosecutors employ, I expect that most of these convictions get appealed, but the show never goes that far.)
As described at the State of New York Court of Appeals website, the supreme court is the system of trial courts for serious cases. The highest court in New York is the Court of Appeals. It serves the same role as what many other states call a supreme court.