Prep and Line: Start by lining a large baking sheet with parchment paper. Cut the chicken breasts into 1-inch pieces.
Dredging Station: Set up three shallow bowls in a line: one with flour, the next with beaten eggs, and the last with panko breadcrumbs. Season the flour with salt, pepper, garlic powder, and paprika.
Bread the Nuggets: Dip each piece of chicken first in the flour mixture, then in the eggs, and finally in the panko breadcrumbs, pressing gently to make sure the breadcrumbs adhere well. Place the breaded chicken pieces on the prepared baking sheet.
Heat the Oil: Heat about 1/2 cup of vegetable oil in a large Dutch oven or skillet over medium-high heat until it reaches 350°F (175°C).
Fry in Batches: Fry the nuggets in batches for 3-4 minutes per side, or until they are golden-brown and crispy. Be careful not to overcrowd the pan.
Drain and Serve: Remove the fried nuggets from the hot oil using a slotted spoon or tongs and place them on a second baking sheet lined with paper towels to drain excess oil.
Combine Ingredients: In a small mixing bowl, whisk together the mayonnaise, ketchup, lemon juice, garlic powder, and smoked paprika until smooth and well-combined.
Chill and Serve: For the best flavor, cover and refrigerate the sauce for at least 30 minutes to allow the flavors to meld before serving with the hot chicken nuggets.