Combine the salmon, 1/2 cup bread crumbs, cheese, corn, mayonnaise, ketchup, and egg in a bowl and mix until combined.
Shape the mixture into 8 patties and coat with the remaining 1/2 cup bread crumbs.
Heat half the oil in a large nonstick skillet over medium heat. Cook the patties until golden brown, 5 minutes.
Add the remaining oil to the skillet, flip the patties and cook an additional 4 to 5 minutes.