Heat an empty large skillet over medium heat until the surface is hot. Place 1 tortilla in the skillet and cook until the underside is warm, about 20 seconds. Flip the tortilla over. Sprinkle the surface with half of the cheese, the turkey, the apple, and then the remaining cheese. Top with the second tortilla.
Cook until the underside is toasted, about 1 1/2 minutes. Flip the quesadilla and cook until the second side is toasted, about 1 1/2 minutes more.
Transfer the quesadilla to a cutting board and cut into 6 wedges. Serve hot, with the salsa, if desired.