1. In a mixing bowl, combine mashed potatoes, egg, flour, cheddar cheese (if using), chives, salt, and pepper. Mix until a cohesive batter forms.
2. Heat oil in a large skillet over medium heat.
3. Scoop 2-3 tablespoons of the potato mixture and form into small patties. Place them in the skillet, a few at a time, without overcrowding.
4. Fry each side for 2-3 minutes until golden brown and crispy. Remove and place on a paper towel to drain excess oil.
5. Serve warm with sour cream, applesauce, or your favorite dipping sauce.