Using the large holes on a grater, shred onion, sweet potato, and baking potatoes into large bowl. Stir egg, flour, salt, and pepper into mixture until well combined.
Heat a little less than 1/4 inch vegetable oil in large frying pan over medium-high heat. When oil is hot, spoon heaping tablespoons of potato mixture into oil and flatten slightly. Fry until golden brown on bottom, turn, and fry the other side (about 3 minutes per side). Drain on paper towels. Repeat with remaining mixture. Serve with sour cream and applesauce, if desired.