In a bowl, mix shredded chicken with BBQ sauce until well coated. Set aside.
Lay out tortillas and sprinkle half of each with 1/2 cup cheddar cheese. Top cheese with BBQ chicken mixture, red onion, and cilantro.
Fold tortillas in half to create half-moon shapes. Press down gently to seal.
Preheat air fryer to 375°F. Spray both sides of quesadillas lightly with cooking spray. Place in air fryer basket without overlapping, working in batches if needed.
Cook for 6-8 minutes, flipping halfway through, until golden brown and cheese is melted. Cut into wedges and serve with sour cream.