In a large, deep bowl, whisk together flour, paprika, cayenne, salt, and pepper. In a large bowl, beat eggs with 2 tablespoons water. Using tongs, place chicken in egg mixture, roll in flour mixture, and shake off excess. Fry chicken in 2 batches until golden brown and cooked through, 6 to 8 minutes (internal temperature should read 165º). Bring oil back to 350º before adding last batch.