  We consider an incarnation of left-right symmetric model with a local gauge
symmetry of $SU(3)_C \otimes SU(2)_L \otimes U(1)_L \otimes SU(2)_R \otimes
U(1)_R$. Heavy scalars and fermions present in the {\bf 27} of $E_6$ are
included in the matter sector along with the Standard Model fermions. Two such
colour singlet fermions, $N$ and $l_S$, transforming as bi-doublet and singlet
under $SU(2)$s respectively, can be potential candidates for Dark Matter (DM).
Assignment of $U(1)$ charges for the matter fields restricts some of the exotic
fermions to interact with the SM fermions. We study in some details the
prospect of such fermionic dark matters by calculating relic densities and
direct detection cross-sections by treating these particles as stand alone
relic particles in turn. $N$, when treated as relic particle, would produce a
direct-detection cross-section very high compared to the experimental upper
limits. However, the interaction rate of $N$ can be controlled by introducing a
dimension-6 operator involving two $N$ fields and two SM fermions and
appropriately choosing the coupling constant. This in turn, makes the
interaction rate of $N$ very high and yields a small relic density. On the
other hand, $l_S$ for some chosen mass window, can give us right amount of
relic, but its direct detection cross-section is too small. Keeping these in
mind, we propose two-component model of DM, where both $N$ and $l_S$ contribute
to the relic density, albeit with unequal proportion while the direct detection
cross-section limits can be satisfied mainly by $N$ in presence of an extra
dimension-6 interaction. We derive limits on such an interaction from XENON
experiment.
