1. Sprinkle fish lightly with salt and dredge in flour on both sides to coat. Warm 1 Tbsp. each oil and butter in a large skillet over medium-high heat until butter melts. Sauté 2 fillets, turning once, until browned on both sides and cooked through, 3 to 4 minutes total. Transfer to a plate; cover with foil to keep warm. Repeat with another Tbsp. oil and butter and remaining fish.
2. Pour wine and lemon juice into skillet and bring to a boil. Remove from heat and stir in capers, parsley and remaining 1 Tbsp. butter; keep stirring until butter melts. Place each fillet on a plate, pour sauce over fish and serve immediately.