Heat oil in a 4 quart heavy pot over moderate heat until deep-fry thermometer registers 375 degrees F.
Stir together 1 tablespoon the salt and 1/4 teaspoon of paprika in a small bowl.
Make batter and fry fish: Pat sole dry, then cut crosswise on a diagonal into 1/2-inch wide strips.
Whisk together flour, 1/4 teaspoon of remaining paprika, 3/4 teaspoon salt, and 1/4 teaspoon pepper, then whisk in seltzer. Working with 6 pieces at a time, dredge fish first in 1/4 cup instant flour, pat off excess. Then dip in batter to coat, shaking off excess, and fry, turning occasionally, until golden brown and fish is just cooked through (cut a piece open to test), 2 to 4 minutes. Transfer with a slotted spoon to paper towels to drain, then sprinkle with some of paprika salt. Skim any bits of fried batter from pot and return oil to 375 degrees F between batches.
Serve with remaining paprika salt on the side, for dipping.