Place squash and onion in a colander; sprinkle with salt and drain until no longer moist, about 30 minutes. Wrap vegetables in a clean kitchen towel and squeeze out as much moisture as possible.
Mix squash and onion mixture, cheese, flour, cornmeal, and egg in a bowl; season with pepper.
Heat oil in a skillet over medium heat. Drop squash mixture by heaping tablespoonfuls into the skillet; cook patties until crisp and golden brown, about 3 minutes per side.
