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We have studied the $CP$ violation discovery reach in neutrino oscillationexperiment with superbeam, neutrino factory and monoenergetic neutrino beam.For NSI satisfying model-dependent bound for shorter baselines (likeCERN-Fr\'ejus set-up ) there is insignificant effect of NSI on the thediscovery reach of $CP$ violation due to $\delta$. Particularly, for superbeamand neutrino factory we have also considered relatively longer baselines forwhich there could be significant NSI effects on $CP$ violation discovery reachfor higher allowed values of NSI. For monoenergetic beam only shorter baselinesare considered to study $CP$ violation with different nuclei as neutrinosources. Interestingly for non-standard interactions - $\varepsilon_{e\mu}$ and$\varepsilon_{e\tau}$ of neutrinos with matter during propagation in longerbaselines in superbeam, there is possibility of better discovery reach of $CP$violation than that with only Standard Model interactions of neutrinos withmatter. For complex NSI we have shown the $CP$ violation discovery reach in theplane of Dirac phase $\delta$ and NSI phase $\phi_{ij}$. The $CP$ violation dueto some values of $\delta $ remain unobservable with present and near futureexperimental facilities in superbeam and neutrino factory . However, inpresence of some ranges of off-diagonal NSI phase values there are somepossibilities of discovering total $CP$ violation for any $\delta_{CP}$ valueat $5 \sigma$ for neutrino factory. Our analysis indicates that for some valuesof NSI phases total $CP$ violation may not be at all observable for any valuesof $\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.

The Discovery reach of $CP$ violation in neutrino oscillation with non-standard interaction effects