Combine the flour, baking powder, cornstarch, salt, and pepper in a large bowl.
Slowly add the cold beer and sparkling water to the dry ingredients, whisking with a fork until the batter is smooth. Be sure to use the batter immediately after mixing.
In another large flat bowl, add some extra flour for dredging the fish.
Cut each of the four fish fillets in half. Blot the fish to remove excess moisture.
Dredge the fish thoroughly in the flour-only bowl and shake off the excess.
Dip the fish into the beer batter to coat all sides evenly. Allow some of the excess batter to drip off the fillets.
Fill a medium-sized skillet with about an inch of vegetable oil. Heat the oil to 350°F - 375°F, using a thermometer to measure the temperature. When the oil is to temperature, carefully place the fish into the oil.
Fry the fish for about 2 minutes on each side until the fillet is nicely golden brown.
Carefully remove the fish with a tongs or slotted spoon, letting the oil drip off, then place the fried fish on paper towels for a few minutes.
Serve immediately!