Rinse catfish and pat dry with paper towels. Pour peanut oil into 5-quart Dutch oven and heat to 350º F on a deep fry thermometer. While peanut oil is heating, whisk together flour, cornmeal, cayenne pepper, salt and black pepper until well-combined. Lightly coat both sides of catfish into flour mixture and then carefully place into Dutch oven, frying only two at a time, until lightly browned, about 5-8 minutes. Remove from Dutch oven and place onto a paper towel lined plate to drain. Serve immediately.