  We have studied the $CP$ violation discovery reach in neutrino oscillation
experiment with superbeam, neutrino factory and monoenergetic neutrino beam.
For NSI satisfying model-dependent bound for shorter baselines (like
CERN-Fr\'ejus set-up ) there is insignificant effect of NSI on the the
discovery reach of $CP$ violation due to $\delta$. Particularly, for superbeam
and neutrino factory we have also considered relatively longer baselines for
which there could be significant NSI effects on $CP$ violation discovery reach
for higher allowed values of NSI. For monoenergetic beam only shorter baselines
are considered to study $CP$ violation with different nuclei as neutrino
sources. Interestingly for non-standard interactions - $\varepsilon_{e\mu}$ and
$\varepsilon_{e\tau}$ of neutrinos with matter during propagation in longer
baselines in superbeam, there is possibility of better discovery reach of $CP$
violation than that with only Standard Model interactions of neutrinos with
matter. For complex NSI we have shown the $CP$ violation discovery reach in the
plane of Dirac phase $\delta$ and NSI phase $\phi_{ij}$. The $CP$ violation due
to some values of $\delta $ remain unobservable with present and near future
experimental facilities in superbeam and neutrino factory . However, in
presence of some ranges of off-diagonal NSI phase values there are some
possibilities of discovering total $CP$ violation for any $\delta_{CP}$ value
at $5 \sigma$ for neutrino factory. Our analysis indicates that for some values
of NSI phases total $CP$ violation may not be at all observable for any values
of $\delta $. Using a neutrino beam from electron capture process for nuclei
$^{110}_{50}$Sn and $^{152}$Yb, we have shown the discovery reach of $CP$
violation in neutrino oscillation experiment.
