Place chicken drumsticks in a tall or wide pot. Pour in peaches with juice, hoisin sauce, barbeque sauce, ginger, and garlic. Mix with your hands until well blended. Transfer to the refrigerator to marinate, 30 minutes to 4 hours.
Preheat oven to 350 degrees F (175 degrees C).
Spread chicken drumsticks in a baking pan; cover with aluminum foil.
Bake in the preheated oven until an instant-read thermometer inserted near the bone reads 165 degrees F (74 degrees C), about 30 minutes.