Preheat an air fryer to 400 degrees F (200 degrees C) according to manufacturer's instructions.
Combine pulled pork, salsa verde, and cojita cheese in a bowl. Stir until evenly combined.
Place a heaping tablespoon of filling into the bottom half of a tortilla. Make 2 folds on either side of the large fold, creating an envelope shape. Roll it up using the tips of your fingers to tuck the filling in as you go. Repeat with remaining tortillas.
Spray the basket of the air fryer with nonstick cooking spray. Place some burritos in the basket seam side-down, making sure to not overcrowd. Spray the tops of the burritos with cooking spray.
Air fry for for 6 minutes. Repeat with remaining burritos. Serve with additional salsa verde for dipping if desired.