Bring 6 cups of generously salted water to a boil in a medium saucepan. Add the frozen peas and cook for 4 minutes. Reserve 3 tablespoons of the hot cooking water, and then drain the peas and return them to the pan. Immediately add the butter, lemon zest and cooking water and season with salt and pepper. Roughly mash the peas with a potato masher or in a food processor, and then cover and set aside.
Heat 2 inches of oil to 300 degrees F in a Dutch oven or heavy-bottomed wide pot. Meanwhile, rinse the potatoes with cold water to remove some of the surface starch and then dry well. Blanch the potatoes, in 2 to 3 batches to avoid overcrowding the pot, until just cooked through but still blond, about 2 minutes. Transfer to a paper-towel-lined baking sheet.
Raise the temperature of the oil to 345 degrees F. Preheat the oven to 200 degrees F. Whisk together 1 1/2 cups of the all-purpose flour, the rice flour, baking soda and 1 teaspoon salt. Pour in the beer, sparkling water and lemon juice and mix just until combined (do not over-mix). Keep the batter refrigerated until ready to use.
When the oil is ready, fry the potatoes in 2 to 3 batches until they are crisp and golden brown, about 3 minutes. Drain on a paper towel-lined baking sheet and sprinkle with salt, and then transfer to the oven to keep warm.
Sprinkle the fish fillets with salt and pepper. Coat the fish in the remaining all-purpose flour and then dip into the batter to completely coat. Carefully swish the fish partway into the oil for a few seconds before completely releasing. Once the coating starts to set on the first fillet, you can add another battered fillet into the oil. Fry until the fish is puffed, golden brown and cooked through, 5 minutes for thin fillets or 7 minutes for thick fillets, and then transfer to a paper towel-lined plate. Cook the remaining fillets and sprinkle with salt.
To serve, reheat the mushy peas if necessary. Serve the fish with the chips, mushy peas and malt vinegar on the side.