Pat the white fish fillets dry with paper towels and season both sides with salt and black pepper.
Heat olive oil in a large non-stick skillet over medium-high heat until shimmering.
Place the fish fillets in the skillet and cook without moving for 3 to 4 minutes until the edges are opaque and the bottom is golden brown.
Carefully flip the fillets and cook for another 3 to 4 minutes until the fish is cooked through and flakes easily with a fork.
Remove the fish from the skillet and set aside on a warm plate.
Reduce the heat to medium and add the butter to the same skillet.
Once the butter has melted, add the minced garlic and cook for 30 seconds until fragrant, stirring constantly to avoid burning.
Stir in the lemon juice and lemon zest, then remove the skillet from heat.
Pour the lemon butter sauce over the cooked fish fillets.
Garnish with chopped fresh parsley and serve immediately.