Combine ground chicken, bread crumbs, Parmesan cheese, egg, garlic, and Worcestershire sauce in a bowl until evenly combined. Form chicken mixture into patties and place in refrigerator to allow patties to firm up, 15 minutes to 1 hour. Preheat oven to 375°F (190°C). Coat air fryer rack or basket with cooking spray and add chicken patties. Cook patties in air fryer until fully cooked, about 18 minutes. A thermometer inserted near the center should read at least 165°F (75°C).