CP violation in the quark sector has been established, which is described by the CKM phenomenon, and we are entering the precision era as far as Flavor physics is concerned. Accumulation of more data from the LHCb and Belle II experiments will, hopefully, guide us
to the pathways to physics beyond the standard model. Unfortunately, the tiny CP asymmetry observed in the quark sector cannot explain the overserved baryon asymmetry
of the Universe. In this context, it is widely believed that leptonic CP violation could be the salvage. Interestingly, the measured non-zero value of $\theta_{13}$ has opened the door of optimism. Needless to mention, the determination of CP violating phase $\delta_{CP}$ is the prime target of most of the current and upcoming neutrino experiments. Unfortunately, non-standard interactions can be a spoiler for the clean determination of the CP phase. We explore, the effect of non-standard interaction and study the prospects of its effect in the future experiments DUNE and T2HK, taking inputs from the currently running long baseline experiments, i.e., T2K and NOvA. Considering non-standard interaction effects from $e-\mu$ and $e-\tau$ sectors, we find interesting results concerning the probabilities, the octant of the $\theta_{23}$, and the CP sensitivities, and therefore, a better understanding of the effects will be crucial for the cleaner determination of $\delta_{CP}$.