  Using cyclotomic classes of order twelve for certain finite fields, we
construct an infinite family of almost difference sets and normally regular
graphs applying the theory of cyclotomy. We show that in each of these fields
neither the multiplicative cyclic subgroup $C$ of index twelve nor $C\cup
\{0\}$ forms an almost difference set, but a union of cosets of $C$ provides us
an almost difference set. We also calculate the intersection numbers and
character tables of cyclotomic association schemes of class two, three and four
obtained from these fields.
