Pat dry fish with paper towels and place on a baking tray or plate. Lightly season with salt and pepper to taste. Set aside.
Then, melt the butter in a saucepan over medium-low heat. If using olive oil, you can skip this step and mix all the marinade ingredients in a small bowl.
Add the garlic, stirring for about a minute, and be careful not to burn it. Then add the paprika, basil, parsley, and lemon juice. Mix well, then adjust seasonings to taste.
Marinate fish on both sides, reserving some to brush on the fish towards the last few minutes of grilling.
While the fish marinates, clean the grill grates thoroughly and lightly oil them to prevent the fish from sticking.
Preheat your grill to medium-high heat. (375-400°F/190-205℉). If using a charcoal grill, make sure the coals are evenly lit and glowing.
Place marinated fish fillets directly on the preheated grill grates. Cook for about 4-6 minutes per side, depending on the thickness of the fillets.
Use a fish spatula or tongs to carefully flip the fillets halfway through the cooking time.
Rockfish is cooked when it becomes opaque and flakes easily with a fork. The internal temperature should be 145°F/63°C.
Remove the fish from the grill, garnish it with parsley, and serve.