No, it's not a snapper, but it doesn't look like a map turtle either. It's too far away for a good ID, but it's shaped like one of the standard basking species, Trachemys, Pseudemys, and Chrysemys. The latter (painteds) naturally range into all areas of NYState. Sliders and cooters are often kept as pets and then released when they get large. So any of those three genera would be likely.