  In a bid to simultaneous explanation of dark matter (DM) and tiny but
non-zero masses of left-handed neutrinos, we propose a minimal extension of the
Standard Model (SM) by a vector-like fermion doublet and three right handed
(RH) singlet neutrinos. The DM arises as a mixture of the neutral component of
the fermion doublet and one of the RH neutrinos, both assumed to be odd under
an additional $\mathcal{Z}_2$ symmetry. As a result, the DM emerges to be a
dominantly Majorana particle and escapes from $Z$-mediated direct search
constraints to mark a significant difference from singlet-doublet Dirac DM. The
other two $\mathcal{Z}_2$ even heavy RH neutrinos give rise masses and mixing
of light neutrinos via Type-I Seesaw mechanism. The particle content
automatically allows us to extend the model by a gauged $U(1)_{B-L}$ symmetry,
which is anomaly free and brings an additional portal between DM and SM
particles. Relic density and direct search allowed parameter space for both the
cases are investigated through detailed numerical scan, while collider search
strategies are also indicated.
