Have the fishmonger scale and remove the heads from the fish. Wash and clean the fish and pat them dry with paper towels. Preheat 2 inches of oil for frying to 375 degrees in a deep, heavy skillet. While the oil is heating, mix the cornmeal, flour, salt, and pepper and coat both sides of the fish with the mixture. Place the butterfish in the hot oil and fry for 5 to 8 minutes, turning occasionally so that both sides are well browned. Drain them on paper towels and serve hot. They are as good for breakfast accompanied by grits and biscuits as they are for dinner with smothered cabbage or collard greens and cornbread.