In a large bowl, combine the mashed potatoes, flour, egg, salt, black pepper, garlic powder, and green onions. Mix until well combined and a dough forms.
Heat the vegetable oil in a large skillet over medium heat.
Scoop about 1/4 cup of the potato mixture and shape it into a patty. Repeat with the remaining mixture.
Once the oil is hot, carefully place the patties in the skillet, making sure not to overcrowd the pan. Fry for about 4-5 minutes on each side, or until golden brown and crispy.
Remove the potato cakes from the skillet and place them on a paper towel-lined plate to drain excess oil.
Serve warm with sour cream, applesauce, or your favorite dipping sauce.