Cut the potatoes into 1/4-inch thick sticks. Place into a large bowl and cover completely with cold water for 20 minutes.
Make the fry sauce: In a bowl whisk all the ingredients together. Refrigerate until ready to serve.
Make Tartar Sauce: Combine mayonnaise, relish, capers, and lemon juice. Season with salt and pepper to taste. Set aside.
Prep lettuce and tomato for the sandwich per the instructions above.
Drain the potatoes well and pat dry with a towel.
Blanch the fries:
If using the oven, heat the oven to 350°F (177°C). Place fries on a parchment-lined baking sheet. Cook in the oven until tender, about 15 to 20 minutes.
If using oil: heat the oil to 300°F (150°C) in a dutch oven or deep fryer. Fry fries in small batches until softened, about 6 to 10 minutes.
Once the fries are soft, set them aside to cool completely.
Prep fish batter: Combine flour, cornstarch, kosher salt, baking powder, paprika, and a few grinds of pepper in a large bowl then whisk to combine.
Fry the fries: Heat the oil to 375°F (190°C) in a dutch oven or deep fryer (or increase the heat if you blanched the fries in oil). Add the cooled fries to the oil in small batches and cook until crispy and golden brown (overcrowding the oil will result in limp fries). Remove to a paper towel-lined large bowl and season with salt immediately to taste.
Batter and fry the fish: Add beer or club soda to the flour/cornstarch mixture and whisk until a batter is just formed. A few small lumps of dry flour are ok. Transfer fish to batter and turn to coat. Working one piece at a time, pick up the fish and allow excess batter to drip back into the bowl. Carefully lower it into the hot oil. Repeat with the remaining fish.
Cook, turning the fish until it is golden brown and crisp on all sides, about 6-8 minutes to an internal temperature of 140°F (60°C) degrees using a thermometer. Transfer to a paper towel-lined plate and season immediately with salt.
Lightly toast the bread in a toaster oven.
Assemble the sandwich: Spread the tartar sauce on the inside of the bun or serve on the side. Layer with lettuce, fish, and tomato.
Serve: Enjoy the sandwich with fries, fry sauce, and beer.