Position oven racks in the top and bottom third of the oven and preheat to 425 degrees F.
Arrange the cod in a single layer on a baking sheet. Arrange the fries in a single layer on a second baking sheet. Bake, tossing the fries and rotating the baking sheets front to back and top to bottom halfway through, until the cod and fries are golden and crispy, about 16 minutes.
Meanwhile, melt the butter in a medium saucepan over medium heat. Whisk in the flour, smoked paprika, mustard powder and 1/2 teaspoon salt. Whisk in the beer, half-and-half and hot sauce and bring to a simmer; simmer, until slightly thickened, about 5 minutes. Remove from the heat and stir in the Cheddar until melted.
Divide the cod and fries among 4 plates. Drizzle the fries with half the sauce and sprinkle with the chives. Serve with lemon wedges, malt vinegar and the remaining sauce on the side.
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