Peel the potatoes and cut them into thick sticks, about 1/2 inch wide. Place them in a pot of salted water and bring to a boil. Cook for about 5-7 minutes until they are slightly tender but not fully cooked. Drain and let them cool.
In a large bowl, combine the shredded cheddar cheese, flour, garlic powder, onion powder, paprika, salt, and pepper. Mix well to combine.
Once the potato sticks are cool, take one stick and dip it into the egg, allowing any excess to drip off. Then coat it in the cheese mixture, pressing gently to adhere. Finally, roll it in the breadcrumbs to coat evenly. Repeat with all potato sticks.
Heat oil in a deep skillet or fryer over medium heat. Once hot, carefully add the coated potato sticks in batches, making sure not to overcrowd the pan. Fry for about 3-4 minutes on each side or until golden brown and crispy.
Remove the potato cheese sticks from the oil and place them on a paper towel-lined plate to drain excess oil. Serve hot with your favorite dipping sauce.