Heat a large nonstick skillet over medium heat. Combine flour, salt, and pepper in a large zip-top plastic bag. Combine water and egg white in a shallow dish, stirring with a whisk. Combine breadcrumbs and cornmeal in another shallow dish, stirring with a whisk.
Working with 1 fillet at a time, place fish in bag; seal and shake to coat. Dip in egg white mixture, and dredge in breadcrumb mixture. Repeat procedure with remaining fillets, flour mixture, egg white mixture, and breadcrumb mixture.
Add vegetable oil and butter to pan; cook until butter melts. Add fillets to pan, and cook 5 minutes on each side or until fish flakes easily when tested with a fork. Serve with lemon wedges.