Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Wash the yellow potato and cut it into 1-inch cubes, keeping the skin on for extra fiber and nutrients.
In a small bowl, whisk together the sea salt, black pepper, garlic powder, and smoked paprika.
Place the potato cubes in a bowl and toss with the olive oil and half of the spice mixture until evenly coated.
Pat the chicken drumsticks dry with a paper towel and season them thoroughly with the remaining spice mixture.
Spread the potatoes onto one side of the prepared baking sheet and place the chicken drumsticks on the other side.
Roast in the oven for 25-30 minutes, or until the potatoes are tender and the chicken reaches an internal temperature of 165°F.
Remove the tray from the oven and brush the chicken drumsticks generously with the sugar-free BBQ sauce.
Return the tray to the oven for an additional 3-5 minutes to allow the sauce to caramelize and become sticky.
Serve the BBQ chicken immediately with the roasted potatoes while they are hot and crispy.