Rinse the fillets and dry with absorbent paper. Lightly dust the fillets with seasoned flour.
Heat the clarified butter in a large frying pan over medium-high heat. Add the fish to the frying pan and season with salt and pepper. Fry the fillets until they are lightly browned on both sides. Set aside to drain on absorbent paper. Keep warm.
Discard any fat remaining in the frying pan. Lower the heat under the pan and add the lemon juice. When the juice comes to a boil, remove the pan from the heat and whisk in the chilled butter. Season the sauce with salt and pepper.
Place the fish fillets on heated servings plates and spoon the sauce over the fish.