Heat oil in a large skillet or fryer to 375 degrees or medium high.
in a large bowl combine the egg, crawfish, onions, melted butter, salt and cayenne pepper. Stir in teh flour until blended.
Drop the batter a tablespoon at a time into the hot oil and fry until golden brown all around. Drain on a wire rack over paper towels. Sprinkle lightly with your favorite cajun seasoning while still hot.
For the dipping sauce combine the mayonnaise, ketchup and horseradish in a small bowl and add hot pepper sauce to your liking. Serve with the beignets.