In a large bowl, combine the mashed potatoes, cheddar cheese, green onions, garlic powder, onion powder, salt, black pepper, and paprika. Mix until well combined.
Take a small portion of the potato mixture (about 2 tablespoons) and shape it into a ball. Insert a lollipop stick or skewer into the center of each ball, then flatten slightly to form a lollipop shape. Repeat with the remaining mixture.
Dip each lollipop into the beaten egg, ensuring it's fully coated, then roll it in breadcrumbs until evenly covered.
Heat about 1 inch of vegetable oil in a deep skillet over medium heat. Once the oil is hot, carefully add the lollipops in batches, frying until golden brown on all sides, about 3-4 minutes. Remove and drain on paper towels.
Serve warm with your favorite dipping sauce.