Layer the halved egg whites on a serving tray and set aside.
Place the yolks in a bowl and mash with a fork. Add the mayo, relish, mustard, sugar, salt, white pepper, garlic, parsley, and cayenne if using it. Whip until the filling is smooth without yolk chunks.
Spoon or pipe enough filling into each egg half. Garnish the top with a dusting of paprika or parsley leaf. Chill before serving.