Boil the potatoes until very tender, and then drain well. Thoroughly mash the potatoes, set in a bowl and cool to temperature. Set the fish on paper towel and thoroughly pat dry.
Cut the fish into thin, lengthwise strips. Cut the strips into small pieces and add them along with the corn, onion, garlic, egg, flour, salt and white pepper to the potatoes and mix to combine.
Spread the breadcrumbs on a wide plate. With lightly water-dampened hands, form fish mixture into 8, 3” wide patties. Coat the patties in breadcrumbs, gently pressing the breadcrumbs on to help them adhere.
Place the oil in a large skillet over medium heat. When hot, fry the fish cakes until golden brown and the cod is cooked through, about 4 minutes per side. Serve 2 cakes per person, garnished with lemon wedges. If desired, serve the fish cakes with tartar sauce.