Preheat oven to 425°F (220°C). Line a sheet pan with foil or parchment.
Toss sweet potato wedges and onion with 1 tbsp oil, half the smoked paprika, and a pinch of salt. Spread on one side of the pan.
Rub chicken with remaining oil, paprika, garlic powder, salt, and pepper. Arrange on the other side of the pan.
Roast 20 minutes, brush chicken and some wedges with half the barbecue sauce, then roast 8–12 more minutes until chicken reaches 165°F and potatoes are tender.
Brush remaining sauce on chicken, broil 1–2 minutes for glaze if desired. Sprinkle parsley and serve.