Preheat your air fryer to 370°F (188°C) for 3–5 minutes. A hot basket helps crisp the tortilla fast.
Mix the filling. In a bowl, combine shredded chicken with Buffalo sauce and ranch or blue cheese dressing.
Stir until the chicken is evenly coated. Taste and add salt and pepper if needed.
Assemble the quesadilla. Lay one tortilla flat. Sprinkle half the mozzarella/Jack and half the cheddar over the tortilla, leaving a small border.
Add the Buffalo chicken in an even layer. Top with green onions and celery if using. Sprinkle the remaining cheese, then place the second tortilla on top and press gently.
Brush or spray with oil. Lightly coat the top tortilla with oil.
This encourages browning and a crisp finish. If your basket tends to stick, lightly oil the air fryer grate as well.
Air fry the first side. Carefully transfer the quesadilla to the basket. Cook for 4–5 minutes at 370°F, until the top begins to turn golden and the cheese starts to melt.
Flip and finish. Using a wide spatula, flip the quesadilla.
Lightly oil the now-exposed side. Air fry another 3–4 minutes, or until both sides are crispy and the cheese is fully melted.
Rest and slice. Let the quesadilla rest on a cutting board for 1–2 minutes so the cheese sets slightly. Slice into wedges.
Serve with extra Buffalo sauce, ranch or blue cheese, and a squeeze of lime.