Preheat oven to 350°. Pour oil into a wide, heavy, medium pot to a depth of 2 in. and heat over medium-high heat until temperature reaches 375° on a deep-fry thermometer. Meanwhile, in a medium bowl, mix cornstarch, flour, baking powder, 1/2 tsp. salt, and 3/4 cup club soda until as smooth as pancake batter, adding more club soda if needed.
Working in 3 or 4 batches, drop fish pieces into batter, then carefully lower into oil and fry until golden and crisp, 2 to 3 minutes per batch. Using a slotted spoon, transfer fish to paper towels to drain. Sprinkle with remaining 1 tsp. salt.
Heat rolls in oven until lightly toasted, about 3 minutes. Mix mayonnaise and Sriracha. In a medium bowl, toss lettuces, radishes, carrot, and jalapeño with lime juice and 2 tbsp. oil.
Spread 2 tbsp. mayonnaise mixture on cut sides of rolls. Fill each roll with cod. Top with salad mixture and serve with extra Sriracha if you like.