1. Cut the onion: Remove the top of the onion and peel. Cut into 16ths, being careful not to cut all the way through.
2. Prepare the batter: In a bowl, mix flour, paprika, cayenne, garlic powder, and black pepper. In another bowl, combine buttermilk and beaten eggs.
3. Coat the onion: Dip the onion into the flour mixture, then into the buttermilk mixture, and back into the flour mixture.
4. Fry the onion: Heat oil in a deep fryer to 375°F. Fry the onion for about 10 minutes or until golden brown. Drain on paper towels.
5. Make the dipping sauce: Mix mayonnaise, ketchup, horseradish, paprika, salt, oregano, black pepper, and cayenne pepper in a bowl.
6. Serve: Place the fried onion on a plate and serve with the dipping sauce.