Stir together the mayonnaise, relish, capers, shallot, dill, Dijon, garlic, Worcestershire, lemon zest, lemon juice, all-purpose seasoning, sugar, and black pepper. Taste and add more lemon juice if desired. Cover and refrigerate while you cook.

Place the cut potatoes in a pot of generously salted water. Bring to a gentle boil and cook until fork-tender but not falling apart. Drain carefully and spread on a wire rack to steam-dry and cool completely.

Heat the frying oil to 350°F. Whisk the ¾ cup cornstarch and ¼ cup seasoned flour together. Add ¾ cup ice-cold water, then add more a little at a time until the slurry has the consistency of heavy cream.

Coat the cooled chips in the slurry, letting the excess drip off. Fry in batches for 3 to 4 minutes, until crisp and lightly golden. Drain on a rack, season with salt, and keep warm.

Whisk the 1 cup seasoned flour and ½ cup cornstarch together. Pour in the cold beer and vodka, whisking just until combined. Small lumps are fine; keep the batter cold.

Increase the oil to 365°F so it settles near 350°F after the fish is added. Pat the cod dry, dip each portion into the batter, let the excess drip off, and carefully lower it into the oil.

Fry the cod in batches for 5 to 7 minutes, turning as needed, until deeply golden, crisp, and 145°F in the center. Drain on a rack and season immediately.

Serve the hot fish and chips with lemon wedges and the chilled homemade tartar sauce.