In a large bowl, combine the mashed potatoes, shredded 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. If using lollipop sticks, insert a stick into the center of each ball.
Dip each potato ball into the beaten egg, allowing any excess to drip off, then roll it in breadcrumbs until fully coated.
Heat about 1 inch of vegetable oil in a deep skillet over medium heat. Once hot, carefully add the potato balls in batches, frying until golden brown and crispy, about 3-4 minutes per side.
Remove the lollipops from the oil and drain on paper towels. Serve warm.