Combine flour, cornmeal, egg, onion, and smoked paprika in a bowl. Add salt to taste. Stir in corn and cheese.
Add milk a little bit at a time if needed to make a moist mixture that can still hold its shape. You may not need all of the milk.
Heat oil over medium heat in a large skillet. Spoon 2-3 tablespoons of the corn mixture onto the hot oil and gently flatten with a spatula.
Cook for 3-4 minutes or until golden, flip and cook an additional 3-4 minutes.
Top with sour cream for serving.
