Recent anomalies observed in NOA and T2K experiments within the framework of standard three-flavor neutrino oscillations suggest the possibility of physics beyond the Standard Model (SM). In this study, we investigate the potential violation of Leggett-Garg type inequalities (LGtI) in the context of three-flavor neutrino oscillations, focusing on scenarios involving complex Non-Standard Interactions (NSI) with or couplings in long baseline accelerator experiments, considering both normal and inverted mass ordering. Our analysis reveals that LGtI violation is significantly enhanced in the normal ordering (NO) for the scenario. At the same time, it is suppressed for the scenario in T2K, NOA, and DUNE experiments. Moreover, we find that in the case of inverted ordering (IO), the DUNE experimental setup above 6 GeV exhibits LGtI violation, suggesting the possibility of the new physics scenario. These findings shed light on the potential of LGtI as a probe for physics beyond the Standard Model in neutrino oscillation experiments.