In a small bowl combine the garlic, lemon juice and rosemary and mix well; set aside. Melt one knob butter in a frying pan over a medium heat.
Meanwhile, pat the fish dry with kitchen paper. Season the fillets with salt and pepper and rub into the flesh. Place the flour on a plate then dredge the fish in the flour. Transfer immediately to the hot pan, skin side down, and fry until the skin is golden brown, about 5 to 8 minutes. Remove the pan from the heat then flip the fish over and cover to keep the heat in, allowing to cook through until the fish flakes easily with a fork, about 5 to 8 minutes. Place on a serving plate and cover with tin foil to keep warm.
Return to the lemon juice, drain and save only the juice. Melt the remaining butter in the same frying pan that the fish was cooked in, add a little salt and pepper and pour in the lemon juice. Bring to a simmer then pour over the fish and serve immediately.