We give an algorithm which produces infinitely many pairwise exotic Stein fillings
of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk.
Furthermore, we determine the support genera of their boundary contact 3-manifolds under some condition.
As a corollary, for a large class of Stein fillings, we realize topological invariants
(fundamental group, homology group, homology group of the boundary, and intersection form)
of each filling as those of infinitely many pairwise exotic Stein fillings