Hard boil eggs. I place the eggs in cold water in a pot, bring it to a boil and continue to boil for 2 minutes. Then I remove from heat and cover for 7 minutes. Rinse under cool running water to keep the yolk from turning dark. Tap the eggs to make peeling easier, and peel them while they are still warm. Cut them in half lengthwise, placing the yolk in a separate bowl.
Place the egg yolks, mayonnaise, mustard, pickle relish, apple cider vinegar, onion, and cayenne, salt and pepper to taste in a bowl. Mix well.
Spoon the yolk mixture into the egg-white halves neatly, filling the inside. Sprinkle the top with the paprika for color.