Pulse all sauce ingredients in a blender until parsley is finely chopped.
Stir together cornmeal, 1/4 teaspoon salt, 1/4 teaspoon pepper, and 1/4 teaspoon cayenne in a shallow bowl. Stir together flour, 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper and 1/4 teaspoon cayenne in another shallow bowl. Lightly beat together eggs, milk, and remaining 1/4 teaspoon salt in a third shallow bowl.
Pat fish dry and dip fillets, 1 at a time, in flour, shaking off excess, then dip in egg mixture, letting excess drip off, and dredge in cornmeal until evenly coated. Arrange fish in 1 layer on a sheet of wax paper.
Heat oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then fry fillets, 2 at a time, turning over once, until golden and just cooked through, 3 to 4 minutes per batch. Transfer to a paper-towel-lined plate to drain. Serve fish with sauce.
