Stir buttermilk and paprika together in a measuring cup until well blended.
Place chicken tenders in a large plastic bag. Pour the buttermilk mixture over the chicken and massage the bag until the chicken is fully covered. Refrigerate for 2 to 24 hours.
Preheat oven to 375 degrees F (190 degrees C).
Combine 1/2 cup bran, bread crumbs, cheese, salt, and garlic powder in a shallow bowl.
Drain the buttermilk mixture from the chicken and discard. Place the chicken tenders in the crumb mixture and coat well, turning to cover each side. Spread the remaining bran down the center of a baking sheet. Place the chicken tenders on the bran.
Bake in the preheated oven until the chicken is no longer pink in the center, 15 to 20 minutes.