Place the potatoes into a large bowl and cover completely with cold water for 20 minutes.
Make tartar sauce: Combine all ingredients until fully combined. Season with salt and pepper to taste. Refrigerate until ready to use.
Blanch the fries.
If using the oven: Heat the oven to 350°F (176°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. Heat the oil to 375°F (190°C).
Prep fish batter: Combine flour, cornstarch, baking powder, and paprika, and season with salt and pepper in a large bowl, then whisk to combine.
Fry the fries: Cook the fries in small batches 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: Stir in the beer a little at a time (or club soda) to the flour/cornstarch mixture until a thick 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) using a thermometer. Transfer to a paper towel-lined plate and season immediately with salt.
Serve the fish with tartar sauce, lemon wedge, french fries, ketchup, and beer.