Heat the vegetable oil to 365 F in a heavy skillet. Make sure it covers one inch up the skillet.
Combine the dry ingredients (flour, baking powder, salt, sugar, and paprika) in a medium-sized bowl.
Whisk together the wet ingredients (egg, milk, and melted butter) in a small bowl and stir them into the flour mixture. Do not overmix the batter.
Add the drained whole kernel corn, chopped parsley, sliced green onions, and shredded cheese. Stir to combine. Do not overmix the batter.
Working in batches, drop ¼ cup mounds of batter into the hot oil and fry for 2 minutes on each side. Remove with a slotted spoon and place on a plate lined with paper towels to absorb any excess oil.