  We explore a gauged $U(1)_{B-L}$ extension of standard model with inclusion
of three right-handed neutrinos of exotic $B-L$ charges to cancel the gauge
anomaly. Non-trivial transformation of new particles under $B-L$ symmetry
forbids the neutrino mass at tree level and hence a small Dirac mass can be
generated radiatively at one loop with a doublet fermion and singlet scalar. We
also discuss the phenomenology of a scalar dark matter, which can be obtained
from the mixing of neutral CP even component of a doublet and real singlet
scalar. An adhoc $Z_2$ symmetry is required in the current framework to
stabilize the dark matter candidate. Presence of new particles with $Z_2$ odd
charges and small mass splitting, makes the phenomenology more interesting by
governing the relic density with co-annihilation processes. We explore the
spin-independent direct detection constraints on dark matter via the scalar
mediation. The new particle spectrum not only opens up new window for dark
matter study but also satisfy the constraints from lepton flavor violating
decay of $\mu \rightarrow e \gamma$.
