Place eggs in a saucepan and cover with water. Bring to a boil, then remove from heat and let eggs stand in hot water for 10 minutes. Remove eggs from hot water, cool under cold running water, and peel.
Cut eggs in half lengthwise. Remove yolks and place in a mixing bowl. Mash yolks with a fork and stir in mayonnaise, mustard, vinegar, salt, and pepper. Fill egg whites with yolk mixture and sprinkle with paprika.