Place eggs in a saucepan and cover with water. Bring to a boil; cook for 8 minutes. Remove from heat and let eggs stand until water is lukewarm, about 15 minutes. Cool eggs under cold running water and peel. Cut eggs in half lengthwise. Place yokes in a bowl. Mix mayonnaise, red onion, dill pickle juice, relish, fresh dill, and mustard together with the egg yolks. Spoon mixture evenly into egg whites. Sprinkle paprika on top.