Preheat an oven to 400 degrees F (200 degrees C). Combine the paprika, parsley, sugar, mustard, salt, and pepper in a small bowl; set aside.
Place the chicken pieces in a 9x13 inch baking dish, and coat with the vegetable oil; arrange skin-side up. Sprinkle evenly with the spice mixture.
Bake the chicken in the preheated oven until no longer pink at the bone and the juices run clear, about 45 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
