In a food processor, combine the shrimp, breadcrumbs, green onions, cilantro, garlic, salt, black pepper, paprika, and cayenne pepper. Pulse until the mixture is well combined but still slightly chunky.
Transfer the mixture to a bowl and stir in the egg until fully incorporated.
Cover the bowl and refrigerate the mixture for at least 30 minutes to help it firm up.
Heat about 2 inches of vegetable oil in a deep skillet or pot over medium heat until it reaches 350°F.
While the oil is heating, form the shrimp mixture into small balls, about 1 inch in diameter.
Once the oil is hot, carefully drop the shrimp balls into the oil in batches, making sure not to overcrowd the pan. Fry for about 3-4 minutes or until golden brown and cooked through.
Remove the shrimp balls with a slotted spoon and drain on paper towels.
Serve warm with your favorite dipping sauce, such as sweet chili sauce or a spicy mayo.