  Recent $\nu_e$ appearance data from the Mini Booster Neutrino Experiment
(MiniBooNE) are in support of the excess of events reported by the Liquid
Scintillator Neutrino Detector (LSND), which provides an indirect hint for the
existence of eV-scale sterile neutrino. As these sterile neutrinos can mix with
the standard active neutrinos, in this paper we explore the effect of such
active-sterile mixing on the determination of various oscillation parameters by
the currently running long-baseline neutrino experiments T2K and NO$\nu$A. We
find that the existence of sterile neutrino can lead to new kind of
degeneracies among these parameters which would substantially deteriorate the
mass hierarchy sensitivity of NO$\nu$A experiment. We further notice that the
inclusion of data from T2K experiment helps in resolving the degeneracies. The
impact of new CP violating phases $\delta_{14}$ and $\delta_{34}$ on the
maximal CP-violation exclusion sensitivity for NO$\nu$A experiment has also
been illustrated. Finally, we discuss the implication of such light sterile
neutrinos on neutrinoless double beta decay processes in line with recent
experimental results, as well as on the sensitivity reach of future
experiments.
