Combine egg, bread crumbs, cherries or cranberries, chopped green onions, and pepper in a mixing bowl. Add ground ham and ground beef; mix well. Shape into 1-inch balls.
Place in a 15x10x1-inch baking pan. Bake in a 350 degree F oven for 15 to 18 minutes or until done. Drain, if necessary.
Meanwhile, heat jelly and mustard together in a chafing dish, blazer pan, or small skillet, stirring occasionally until jelly is melted. Add ham balls to chafing dish. (Or, transfer ham balls to a warm heatproof serving bowl and pour glaze over ham balls.) Keep warm. Garnish with green onion slivers. Makes 48 meatballs (48 appetizer servings).