  In this continuation of \cite{BK} we investigate the non-abelian Hodge
correspondence on compact Sasakian manifolds with emphasis on the quasi-regular
case. On quasi-regular Sasakian manifolds, we introduce the notions of
quasi-regularity and regularity of basic vector bundles. These notions are
useful in relating the vector bundles over a quasi-regular Sasakian manifold
with the orbibundles over the orbifold defined by the orbits of the Reeb
foliation of the Sasakian manifold. We note that the non-abelian Hodge
correspondence on quasi-regular Sasakian manifolds gives a canonical
correspondence between the semi-simple representations of the orbifold
fundamental groups and the Higgs orbibundles on locally cyclic complex
orbifolds admitting Hodge metrics. Under the quasi-regularity of Sasakian
manifolds and vector bundles, we extend this correspondence to one between the
flat bundles and the basic Higgs bundles. We also prove a Sasakian analogue of
the characterization of numerically flat bundles given by Demailly, Peternell
and Schneider.
