  We present a detailed discussion on neutrinoless double beta decay $(0\nu
\beta \beta)$ within left-right symmetric models based on the gauge symmetry of
type $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ as well as $SU(3)_L \times
SU(3)_R \times U(1)_{X}$ where fermion masses including that of neutrinos are
generated through a universal seesaw mechanism. We find that one or more of the
right-handed neutrinos could be as light as a few keV if left-right symmetry
breaking occurs in the range of a few TeV to 100 TeV. With such light
right-handed neutrinos, we perform a detailed study of new physics
contributions to $0\nu \beta \beta$ and constrain the model parameters from the
latest experimental bound on such a rare decay process. We find that the new
physics contribution to $0\nu \beta \beta$ in such a scenario, particularly the
heavy-light neutrino mixing diagrams, can individually saturate the existing
experimental bounds, but their contributions to total $0\nu \beta \beta$
half-life cancels each other due to unitarity of the total $6\times 6$ mass
matrix. The effective contribution to half-life therefore, arises from the
purely left and purely right neutrino and gauge boson mediated diagrams. We
find that the parameter space saturating the $0\nu \beta \beta$ bounds remain
allowed from the latest experimental bounds on charged lepton flavour violating
decays like $\mu \rightarrow e \gamma$. We finally include the bounds from
cosmology and supernova to constrain the parameter space of the model.
