Neutrino oscillations in matter offer a novel path to investigate new physics. One of the main goals of neutrino experiments is to determine the CP phase and the presence of new physics can alter the scenario. We assume that the observed difference, if any, in the CP phase is due to the possible non-standard interactions. We derive the relevant coupling strengths using the simulated data sets of NO$\nu$A and T2K and study their effects in the next generation long-baseline experiments: T2HK and DUNE. Our analysis show significant impact on the sensitivity of atmospheric mixing angle $\theta_{23}$ in the normal as well as inverted orderings and also exhibits appreciable difference in probabilities for both the experiments with inclusion of non-standard interaction arising from $e-\mu$ as well as $e-\tau$ sectors.