Preheat your grill for two-zone grilling, setting the temperature to medium-high heat (375-400F).
Season the chicken drumsticks evenly on all sides with garlic salt and black pepper.
Place the chicken legs on the direct heat side of the grill. Cook for 30-35 minutes, flipping them every 5-7 minutes. Grill until the internal temperature of the chicken reaches 165F using a meat thermometer.
Move the grilled drumsticks to the indirect heat side of the grill. Baste them with the Teriyaki BBQ Sauce (or your favorite BBQ sauce).
Grill the chicken for an additional 5-10 minutes on indirect heat. The sauce should set, start to caramelize, and the internal temperature should reach 175F.
Remove the grilled drumsticks from the grill and let them rest for a few minutes. Serve with additional teriyaki BBQ sauce on the side for extra dipping. Enjoy the bbq chicken dish!