Preheat the oven to 400°F and line a large baking sheet with parchment paper.
In a mixing bowl, combine the ground turkey, breadcrumbs, egg, 1/3 cup barbecue sauce, garlic powder, salt, and black pepper. Mix until evenly blended, then divide the mixture into four equal portions and shape each into a small loaf. Place the loaves on one side of the prepared baking sheet.
In a separate bowl, toss the sweet potato wedges with the olive oil and paprika until coated. Spread them in a single layer on the other side of the baking sheet.
Bake for 20 minutes. Remove the pan and brush the tops of the meatloaves with the remaining 2 tablespoons of barbecue sauce. Return the pan to the oven and bake for another 10 to 15 minutes, until the meatloaves reach an internal temperature of 165°F and the wedges are tender.