Begin by laying out three shallow dishes. In the first dish, place the flour. In the second dish, add the beaten eggs. In the third dish, combine the breadcrumbs, garlic powder, paprika, salt, and black pepper.
Take a slice of ham and place a mozzarella stick at one end. Roll the ham around the cheese stick tightly. Repeat this process until all the ham and cheese sticks are prepared.
Heat about 2 inches of vegetable oil in a deep skillet or pot over medium heat until it reaches 350°F.
Dredge each ham and cheese roll in the flour, shaking off the excess. Next, dip it into the beaten eggs, allowing any excess to drip off. Finally, coat the roll in the seasoned breadcrumbs, pressing gently to adhere.
Carefully place the coated rolls into the hot oil, cooking in batches to avoid overcrowding. Fry for about 2-3 minutes on each side or until golden brown and crispy.
Once cooked, remove the sticks from the oil and place them on a paper towel-lined plate to drain excess oil.
Serve warm with your favorite dipping sauce, such as marinara or ranch dressing.