Whisk together the eggs, beer, 1 / 2 teaspoon salt, and 1 / 4teaspoon black pepper in a medium bowl; set aside. In a separate medium bowl, whisk together the flour, remaining teaspoon salt and 1 / 4 teaspoon black pepper, and cayenne; add to the egg mixture. Whisk until the batter is well combined; let rest 15 minutes.
Meanwhile, heat oil in a large cast-iron or heavy skillet until a deep-fry thermometer registers 375F.
Dip the fish strips one at a time into the batter, letting excess drip off. Working in batches, drop carefully into hot oil; fry until the fish is golden and crisp and cooked through, about 4 minutes. Remove with a slotted spoon; drain on paper towels. Serve immediately.