  So far the most sophisticated experiments have shown no trace of new physics
at the TeV scale. Consequently, new models with unexplored parameter regions
are necessary to explain current results, re-examine the existing data, and
propose new experiments. In this Letter, we present a modified version of the
$\mu\nu$SSM supersymmetric model where a non-Universal extra U(1) gauge
symmetry is added in order to restore an effective R-parity that ensures proton
stability. We show that anomalies equations cancel without having to add
\emph{any} exotic matter, restricting the charges of the fields under the extra
symmetry to a discrete set of values. We find that it is the viability of the
model through anomalies cancellation what defines the conditions in which
fermions interact with dark matter candidates via the exchange of $Z'$ bosons.
The strict condition of universality violation means that LHC constraints for a
$Z'$ mass do not apply directly to our model, allowing for a yet undiscovered
relatively light $Z$', as we discuss both in the phenomenological context and
in its implications for possible flavour changing neutral currents. Moreover,
we explore the possibility of isospin violating dark matter interactions; we
observe that this interaction depends, surprisingly, on the Higgs charges under
the new symmetry, both limiting the number of possible models and allowing to
analyse indirect dark matter searches in the light of well defined, particular
scenarios.
