Warm oil in a large skillet over medium-high heat.
In a bowl, whisk together egg and milk. Coat cod fillets with flour; shake off excess. Dip cod in egg mixture; allow excess to drip off. Coat cod with oats.
Place fish one at a time in hot oil; fry about 2 1/2 minutes, then turn over, and fry about 2 1/2 minutes more. Remove to paper towels. Season to taste with salt and pepper.
