In a large pasta pot, bring 8 quarts of water to a boil. Add the potatoes and cook until easily pierced with the point of a paring knife, about 25 minutes. Drain, peel, and, while still warm, pass potatoes through a food mill. Place in a large bowl and immediately add the tuna, ricotta, marjoram, and salt and pepper to taste. Add the egg yolks and mix well to combine. Using tablespoons, form the mixture into golf-ball sized balls and set on a sheet tray.
In a large, heavy-bottomed skillet, heat the oil until almost smoking. While the oil heats, place the flour on a plate, egg whites in a shallow bowl and the bread crumbs on a plate. Dredge the balls first in the flour, then the egg whites, then the bread crumbs and fry in the olive oil until golden brown on all sides. Remove balls from pan with a slotted spoon and let drain on a plate lined with paper towels. Serve immediately.