KBSM for the family of small Seifert fibered 3-manifolds with multiplicity two exceptional fibers

We show that the Kauffman bracket skein module (KBSM) for small Seifert fibered [Formula: see text]-manifolds with singular fibers of multiplicity two is a free module of rank [Formula: see text], where [Formula: see text] is the Euler number, and we construct its basis. This family of [Formula: see text]-manifolds includes as a special case the quaternionic [Formula: see text]-manifold for which KBSM was first computed by J. Harris.