In a mixing bowl, combine the salt, black pepper, garlic powder, and smoked paprika.
Toss the chicken drumsticks in the spice mixture until evenly coated.
Pour 1/2 cup water or chicken broth into the Instant Pot and place the trivet or steaming rack inside if using.
Arrange the seasoned drumsticks on the trivet or directly in the liquid in a single layer or slightly stacked.
Close the lid, set the valve to sealing, and cook on High Pressure for 10 minutes. Allow a 5-minute natural release, then perform a quick release for any remaining pressure.
Carefully remove the drumsticks with tongs and place them in a bowl or on a tray.
Toss the hot drumsticks with 1 cup BBQ sauce until evenly coated, then serve.