Toss zucchini, yellow squash, and carrots with salt in a colander and drain for 15 minutes. Wrap vegetables in a clean kitchen towel and squeeze out as much moisture as possible; transfer mixture to a bowl.
Combine corn muffin mix, baking powder, and paprika in a bowl. Stir in vegetables and eggs until well mixed.
Heat 2 tablespoons vegetable oil in a large skillet over medium heat, tilting skillet to spread oil evenly. Drop tablespoonfuls of the zucchini batter into the hot oil, flattening each dollop with the back of a spoon. Pan-fry until golden brown, 1 to 2 minutes per side.
Transfer fritters to a paper towel-lined plate to drain. Cool slightly before serving.
