  Thanks to high precision long baseline neutrino experiments such as NO$\nu$A
and DUNE, possible effects of Non-Standard neutrino Interactions (NSI) on
neutrino oscillation data have received renewed interest in the last two years.
It is however challenging to build models that can give rise to NSI with
sizeable couplings discernible at neutrino oscillation experiments without
violating the various existing experimental bounds. We introduce two viable
models that can lead to neutral current NSI with sizable couplings. Both models
are based on a new $U(1)^\prime$ gauge symmetry with $Z^\prime$ gauge boson of
mass $O(10~{\rm MeV})$. We will highlight the common phenomenological features
of these models and suggest ways to test them.
