Prepare the snapper by removing the bones, or have them removed when you purchase the filets.
Season both sides with salt and pepper. Then sprinkle both sides with flour.
In a large pan, add 2 tablespoon of extra virgin olive oil and bring to medium-high heat. Once the oil is shimmering, lay the filet into the pan, skin side down. Sear for 3-4 minutes or until skin is golden brown. Using a fish spatula, flip the filets, and sear for another 4 minutes or until they reach an internal temperature of 145°.
Lower the heat to low. Add 2 tablespoon butter, crushed garlic, and thyme, and stir until the foaming subsides. Add in the lemon juice, wine, and capers, and reduce the liquid by half, until you can drag a spoon through and leave a trail. Add the remaining tablespoon of butter and stir until combined.
Pour sauce over each filet and serve.
Notes
Pat the fish to dry to make sure that when you place it in the pan, there is no extra moisture that will cause it to be steamed while cooking.
Snapper has bones. I always prefer to debone prior to cooking so that my guests and I don't have to worry about bones while eating. (Someone will always find a bone or two either way)
Seared fish is a QUICK recipe. You have to be on the fish watching and checking the temperature. The most important thing to do if you're new to cooking fish is to check the temperature with an instant-read thermometer as you go, so you can see exactly when it hits 145 degrees. Just one or 2 extra minutes can add as much as 20 degrees, drying out your fish.
When searing a fish, I always start with the skin side down first. This will result in the crispest layer of skin.