Preheat the oven to 375°F (190°C).
In a mixing bowl, whisk together the ketchup, brown sugar, apple cider vinegar, Worcestershire sauce, minced garlic, paprika, onion powder, salt, black pepper, and cayenne pepper (if using).
Season the chicken drumsticks or thighs with salt and black pepper.
Brush the barbecue sauce over the chicken, making sure to coat each piece evenly.
Place the chicken in a baking dish and bake for 35-45 minutes, or until the chicken is cooked through and the skin is crispy. Baste the chicken with additional barbecue sauce every 10-15 minutes.
Remove the chicken from the oven and let it rest for a few minutes before serving.
Serve the baked barbecue chicken with your favorite sides, such as corn on the cob, coleslaw, or baked beans.