If using frozen fish, thaw completely. If the fish is not already filleted, fillet it.
Season the fillets lightly with salt and a small pinch of sugar.
In a jar with a tight lid, combine oil, oyster sauce, cumin, lemon juice, and green curry paste. Shake vigorously for 1-2 minutes to create an emulsion.
Brush the marinade onto both sides of each fillet. Place in a covered container and refrigerate for at least 2 hours.
Preheat your grill to medium-high heat until the grates are very hot.
Place the fish on the grill and cook for 2-3 minutes per side until cooked through.