Beer-Battered Fish and Loaded Beer Cheese Chips

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Two 12.5-ounce packages frozen beer-battered cod

One 28-ounce package frozen shoestring fries 

2 tablespoons unsalted butter 

2 tablespoons all-purpose flour 

1 1/2 teaspoons smoked paprika 

1 1/2 teaspoons mustard powder 

Kosher salt 

3/4 cup beer 

1/2 cup half-and-half 

Dash hot sauce 

2 cups grated Cheddar  

3 tablespoons chopped chives 

Lemon wedges, for serving 

Malt vinegar, for serving