Remove egg yolks and place into a mixing bowl. Set whites aside. Add mayonnaise, vinegar, relish, mustard, sugar, cayenne, and black pepper to the yolks; mix well with a fork.

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Place mixture into a small resealable zip-top bag and snip the end off one of the corners. Pipe mixture into the egg whites. Sprinkle tops with more black pepper and cayenne. Chill until ready to serve.