In a large bowl, combine 2 cups of mashed potatoes with 1 beaten large egg. Mix until smooth and uniform.
Stir in 1/2 cup grated cheddar, 2 tablespoons chopped chives, 1/2 teaspoon garlic powder, 1 teaspoon salt, and 1/2 teaspoon black pepper.
Add 1/2 cup all-purpose flour a little at a time, stirring until the mixture holds together but is still soft. If the mixture is too wet, add a bit more flour.
Heat 2 tablespoons of oil or a mix of oil and butter in a large nonstick skillet over medium heat until shimmering.
Scoop about 2 tablespoons of the potato mixture per fritter and shape into a patty. Place them carefully into the hot skillet without overcrowding.
Fry for 3–4 minutes per side, or until golden brown and crisp. Flip gently with a spatula to avoid breaking.
Transfer cooked fritters to a paper towel-lined plate to drain excess oil. Keep warm in a low oven if cooking in batches.
Serve hot with sour cream, yogurt, apple sauce, or your favorite dipping sauce. Garnish with extra chives if desired.