Cut the potatoes into 1/4-inch thick sticks. Place into a large bowl and cover completely with cold water for 20 minutes.
Make Tartar Sauce: Combine mayonnaise, relish, capers, and lemon juice. Season with salt and pepper to taste. Set aside.
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 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) using a thermometer. Transfer to a paper towel-lined plate and season immediately with salt.
Make Hot buttered rum: Add the cider to a saucepan over low heat, stirring occasionally until hot. Using an electric mixer, beat the brown sugar, butter, and pumpkin spice in a medium bowl until blended and smooth. Transfer the mixture to a large measuring cup. Add the rum and apple cider. Stir until the butter mixture dissolves. Portion and serve.
Serve the fish with tartar sauce, lemon wedge, french fries, ketchup, and hot buttered rum.