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 from hot water, cool, peel, and cut in half lengthwise.
Remove yolks and place in a mixing bowl. Mash yolks with a fork and stir in mayonnaise, mustard, vinegar, and salt. Fill egg whites with yolk mixture and sprinkle with paprika.