Preheat air fryer to 400°. Peel and cut potato lengthwise into 1/2-in.-thick slices; cut slices into 1/2-in.-thick sticks.
In a large bowl, toss potato with oil, pepper and salt. Place potato pieces in a single layer in air fryer basket; cook until just tender, 5-10 minutes Toss potatoes in basket to redistribute; continue to cook until lightly browned and crisp, 5-10 minutes longer.
Meanwhile, in a shallow bowl, mix flour and pepper. In another shallow bowl, whisk egg with water. In a third bowl, toss cornflakes with cheese and cayenne. Sprinkle fish with salt; dip into flour mixture to coat both sides; shake off excess. Dip in egg mixture, then in cornflake mixture, patting to help coating adhere.
Remove fries from basket; keep warm. Place fish in a single layer in air fryer basket. Cook until fish is lightly browned and just beginning to flake easily with a fork, turning halfway through cooking, 8-10 minutes. Do not overcook. Return fries to basket to heat through. Serve immediately. If desired, serve with tartar sauce.