Squeeze juice from half a lime into a liquid measuring cup. Add other marinade ingredients and mix well.
Place fillets on a plate. Pour marinade on top, spreading to coat evenly. Turn fillets over several times to coat both sides. Cover and let stand 15 minutes.
Heat skillet over medium heat. Add butter and swirl around skillet to melt and coat bottom.
Place fish in the skillet and cook 2 minutes on each side (for thin fillets like flounder), or longer (for thick fillets like cod). Fish is done when it’s opaque and comes apart with a fork.