Preheat grill to medium-high heat (about 425°F). Clean and oil the grates or use a well-oiled grill basket.
Pat the cod dry with paper towels. In a small bowl, mix olive oil, lemon zest, salt, pepper, and smoked paprika. Brush all over the fillets.
Grill the cod over direct heat for 3 to 4 minutes per side, turning carefully with a thin spatula, until opaque and it flakes easily (internal temp 145°F).
While fish grills, melt butter in a small saucepan over medium heat. Add garlic and cook 30 to 45 seconds until fragrant, not browned.
Stir in lemon juice, parsley, dill, and capers. Cook 30 seconds more, then remove from heat. Adjust salt and pepper to taste.
Transfer cod to a platter and spoon lemon-herb sauce over the top. Rest 1 minute to absorb flavors.
Serve immediately with extra lemon wedges and your favorite sides.
Notes
For easy handling, grill the cod in a well-oiled basket or on lightly oiled foil. Swap cod for haddock, halibut, or mahi-mahi. If using salted butter or capers, reduce added salt. Fish is done when it flakes easily and reaches 145°F.