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In this continuation of \cite{BK} we investigate the non-abelian Hodgecorrespondence on compact Sasakian manifolds with emphasis on the quasi-regularcase. On quasi-regular Sasakian manifolds, we introduce the notions ofquasi-regularity and regularity of basic vector bundles. These notions areuseful in relating the vector bundles over a quasi-regular Sasakian manifoldwith the orbibundles over the orbifold defined by the orbits of the Reebfoliation of the Sasakian manifold. We note that the non-abelian Hodgecorrespondence on quasi-regular Sasakian manifolds gives a canonicalcorrespondence between the semi-simple representations of the orbifoldfundamental groups and the Higgs orbibundles on locally cyclic complexorbifolds admitting Hodge metrics. Under the quasi-regularity of Sasakianmanifolds and vector bundles, we extend this correspondence to one between theflat bundles and the basic Higgs bundles. We also prove a Sasakian analogue ofthe characterization of numerically flat bundles given by Demailly, Peternelland Schneider.

Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles