Whisk the flour, lemon-pepper seasoning, granulated garlic, baking powder and 1/2 teaspoon salt in a bowl. Whisk in 1 tablespoon vegetable oil, then 1/2 to 3/4 cup ice water to make a smooth batter. Refrigerate for at least 20 minutes.
Meanwhile, make the tartar sauce: Whisk the mayonnaise, pickle relish, lemon juice, and salt and pepper to taste in a bowl.
Heat 4 to 6 inches of vegetable oil in a deep pot until a deep-fry thermometer registers 375 degrees.
Cut the fish into 8 pieces, about 1 1/2 by 4 1/2 inches. Thread each piece of fish onto a long wooden skewer. Season generously with salt and pepper.
Dip the fish into the batter, turning to coat; let the excess drip off. Carefully place the fish (skewers and all) in the hot oil. Fry, turning as needed with tongs, until golden and cooked through, about 6 minutes. Remove and drain on paper towels; season with salt. Serve with the tartar sauce and lemon wedges.