In a large skillet over medium heat, cook the breakfast sausage, breaking it into small crumbles with a spatula, until fully browned and cooked through, about 8-10 minutes. Drain excess fat and transfer to a large mixing bowl. Let cool for 5 minutes.

To the bowl with the cooked sausage, add the thawed hashbrowns, shredded cheddar (if using), beaten egg, garlic powder, black pepper, salt, and flour. Mix thoroughly until everything is evenly distributed and the mixture holds together when pressed.

Using your hands, scoop about 2 tablespoons of the mixture and roll into a compact ball, then gently flatten slightly into a thick patty or nugget shape, about 1.5 inches wide. Place on a parchment-lined tray. Repeat with remaining mixture; you should have about 20-24 bites.

In a large, deep skillet or Dutch oven, heat about 1/2 inch of vegetable oil over medium-high heat to 350°F (175°C). Working in batches to avoid crowding, carefully place the bites into the hot oil. Fry for 3-4 minutes per side, turning once, until deeply golden brown and crispy. Transfer to a paper towel-lined plate to drain.

While the bites are frying, whisk together all dipping sauce ingredients—sour cream, mayonnaise, maple syrup, Dijon mustard, and smoked paprika—in a small bowl until smooth. Taste and adjust seasoning if desired.

Arrange the hot, crispy hashbrown sausage bites on a serving platter. Place the bowl of dipping sauce in the center or to the side. Serve warm.