Add the shredded chicken to a mixing bowl.
Stir in taco seasoning and salsa, if using.
Lay the tortillas on a clean work surface.
Sprinkle a small amount of cheese over one half of each tortilla.
Add a small spoonful of seasoned chicken.
Sprinkle a little more cheese over the chicken.
Fold each tortilla in half and press gently.
Heat oil or butter in a skillet over medium heat.
Add the folded quesadillas in a single layer.
Cook for 2 to 3 minutes per side, until golden and crisp.
Transfer to a cutting board or wire rack.
Let rest for 1 to 2 minutes before serving.
Cut each folded quesadilla in half, if desired.
Serve warm with salsa, sour cream, or guacamole.