Preheat a griddle or large skillet over medium-high heat.
Place a tortilla on the griddle. Spoon 1/4 cup of ham evenly over half of the tortilla. Top with 1 Tbsp of green pepper, 2 ounces of pineapple, and 1/4 cup of mozzarella. Fold the bare part of the tortilla over the top of the ingredients.
Cook until the bottom begins to brown. Carefully, flip the quesadilla over and continue to cook until the bottom browns and the cheese is melted. Remove from the griddle to a cutting board. Repeat with remaining ingredients.
Cut each quesadilla into 4 slices and serve warm with pizza sauce for dipping, if desired.