Combine the egg and beer in a large bowl.
In a separate bowl, combine the flour, salt, and paprika.
Add the seasoned flour to the beer mixture and gently poke at it with a fork until you have a loose, floppy batter with plenty of lumps. Don't stir, whisk, or mix.
Dip pieces of cod into the beer batter and drop into a shallow frying pan over medium heat for about 2 minutes per side.