Place flour in a shallow bowl and season with salt and black pepper. Place eggs in another shallow bowl. In a third shallow bowl, combine panko, Parmesan, lemon zest, oregano, and cayenne. Season with salt and pepper.
Working one at a time, dip chicken into flour, then eggs, and then panko mixture, pressing to coat evenly.
Place in air fryer basket and cook at 375°F for 10 minutes. Flip chicken, and cook for another 5 minutes, until coating is golden and chicken is cooked through.