Mix grated squash, flour, egg, milk, onion, sugar, 1 teaspoon salt, and pepper in a bowl until well combined.
Heat oil in a pan over medium heat. Working in batches, add tablespoonfuls of the squash mixture to the hot oil. Cook until the edges start to brown, 2 to 3 minutes. Flip patties and cook for 2 to 3 more minutes. Drain on paper towels. Repeat to cook remaining patties.
Serve hot and sprinkle with more salt, if desired.