Preheat oven to 425 degrees.
Rub the redfish fillets with oil, and season the flesh of the fillet with Creole seasoning. Place fillets, skin-side down, on a gas or charcoal grill over medium-high heat. Grill the fish, never turning. Do not worry- the skin and scales will char, flame up, and smoke. Grill fillets approximately six minutes. Place fillets, skin side down, on a baking sheet and continue cooking in the oven for another five minutes. Remove from oven, sprinkle parsley over fish and serve immediately with lemon wedges on the side.