Place the cold mashed potatoes in a large bowl and break up any lumps with a fork. Add the drained corn, shredded cheddar, green onions, garlic powder, salt, and black pepper. Stir until evenly combined. Crack in the egg and mix thoroughly. Add the flour and fold until the mixture holds together. Heat 2 tablespoons of vegetable oil in a skillet over medium heat. Scoop about 2 tablespoons of mixture and shape into a 1/2-inch thick patty. Place into the hot skillet without overcrowding. Cook for 3–4 minutes per side until golden brown and crispy. Add more oil as needed for additional batches. Transfer to a paper towel-lined plate before serving.