Abstract: In this paper, we explore the impact of flavor violating neutral current non-standard interaction (NSI) parameter epsilon(mu tau) in the oscillation of atmospheric neutrinos and antineutrinos separately using the 50 kt magnetized ICAL detector at INO. We find that due to non-zero epsilon(mu tau), nu(mu) -> nu(mu) and (nu) over bar (mu) -> (nu) over bar (mu) transition probabilities get modified substantially at higher energies and longer baselines, where vacuum oscillation dominates. We demonstrate for the first time that by adding the hadron energy information along with the muon energy and muon direction in each event, the sensitivity of ICAL to the NSI parameter epsilon(mu tau) can be enhanced significantly. The most optimistic bound on epsilon(mu tau) that we obtain is – 0.01 < epsilon(mu tau) < 0.01 at 90% C.L. using 500 kt.yr exposure and considering E-mu, cos theta(mu), and E-had' as observables in their ranges of [1, 21] GeV, [- 1, 1], and [0, 25] GeV, respectively. We discuss for the first time the importance of the charge identification capability of the ICAL detector to have better constraints on epsilon(mu t). We also study the impact of non-zero epsilon(mu tau) on mass hierarchy determination and precision measurement of oscillation parameters.