Rinse the chicken drumsticks and pat them dry with paper towels.
Add half of the salt and pepper, making sure each piece is well coated.
Pour the buttermilk over the chicken. Cover the bowl and refrigerate for at least 2 hours.
In a separate bowl, combine the flour, paprika, garlic powder, onion powder, and the remaining salt and pepper to create a seasoned flour mixture.
Remove the drumsticks from the buttermilk, allowing any excess liquid to drip off. Roll each piece in the seasoned flour, pressing the flour onto the chicken to ensure a crispy coating.
Heat vegetable oil in a deep fryer or heavy pot to 350-375°F (175-190°C). Carefully place the coated chicken into the hot oil in small batches, making sure not to overcrowd the fryer.
Fry for 12-15 minutes, or until the chicken is golden brown, crispy, and cooked through (internal temperature should reach 165°F/74°C).
Use a slotted spoon to transfer the fried chicken to a plate lined with paper towels to drain excess oil. Let the chicken cool slightly before serving.