Place eggs in a saucepan, cover with cold water and bring to a boil over medium-high heat. When water boils, remove from heat and cover the saucepan. Let the eggs sit for 16 minutes, then drain and cool eggs in a bowl of ice water. Peel and halve lengthwise.
Scoop out yolks from the whites and place in a mixing bowl. Use a fork to smash the yolks, then add cream cheese, mayonnaise, mustard, relish, and salt to the yolks and stir to combine well.
Pipe or spoon the yolk mixture back into the egg whites. Serve with paprika dusted on top of each egg half.