Place egg in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool, and peel.
Cut eggs in half lengthwise, place the yolks into a mixing bowl, and set the whites aside. Mash the yolks with the deviled ham, mustard, mayonnaise, and black pepper. Spoon or pipe filling into egg white halves. Garnish each deviled egg with an olive slice, then sprinkle with paprika.