Domiciliary residents of a school district who have attained twenty-one (21) years of age may enroll in the school district's adult education programs; but no person over twenty-one (21) years of age shall be permitted to enroll in the public schools of any school district from kindergarten through grade twelve (K-12), except in school districts where no courses are offered for which adults can obtain high school credit and except as provided in § 6-16-306.