In a large mixing bowl, combine the cold mashed potatoes, shredded cheddar cheese, chopped chives, garlic powder, salt, and black pepper.
Add the beaten egg to the potato mixture and stir until the ingredients are thoroughly incorporated.
Form the mixture into small balls, approximately 1 inch in diameter, using about one tablespoon of mixture per puff.
Place the flour in one shallow bowl and the Panko breadcrumbs in another shallow bowl.
Roll each potato ball lightly in the flour, then roll in the Panko breadcrumbs, pressing gently to ensure the crumbs adhere to the surface.
Heat approximately 2 inches of vegetable oil in a deep skillet or saucepan to 350°F (175°C).
Carefully place the potato puffs into the hot oil in batches, ensuring the pan is not overcrowded.
Fry for 2 to 3 minutes, turning occasionally, until the puffs are golden brown and crispy on all sides.
Use a slotted spoon to remove the puffs from the oil and transfer them to a paper-towel-lined plate to drain excess fat.
Serve immediately while hot and crispy.