Grate the zucchini and squeeze out as much moisture as possible using a clean kitchen towel or paper towels.
In a large bowl, combine the zucchini, onion, egg, milk, and corn.
Add the flour, baking powder, dried basil, garlic powder, salt, pepper, and Parmesan cheese. Stir just until combined. If the batter seems too thin, add another tablespoon or two of flour.
Heat about ¼ inch of oil in a large skillet over medium heat.
Drop spoonfuls of batter into the hot oil and gently flatten with the back of a spoon.
Fry for 3 to 4 minutes per side, or until golden brown and cooked through.
Transfer to a wire rack or paper towel-lined plate. Serve immediately, or keep warm on a wire rack in a 200°F oven until ready to serve.