Fill a medium saucepan halfway with water and bring to a boil. Carefully add the eggs and boil for at least 10 minutes. Remove the eggs and place in ice water to cool.
Gently crack and peel off the shell. Cut the eggs in half lengthwise.
Mix in the mayonnaise, mustard, relish, salt and pepper to taste. Sample the mixture and adjust any ingredients to taste, if desired. Stir in ham.
Spoon or pipe the yolk mixture into the eggs whites. Cover and refrigerate for about 30 minutes or until chilled.
Sprinkle with smoked paprika and green onions before serving.