  The recent anomaly observed in NO$\nu$A and T2K experiments, in standard
three-flavor neutrino oscillation could potentially signal physics extending
beyond the standard model (SM). For the NSI parameters that can accommodate
this anomaly, we explore the violation of Leggett-Garg type inequalities (LGtI)
within the context of three-flavor neutrino oscillations. Our analysis focuses
on LGtI violations in scenarios involving complex NSI with $\epsilon_{e\mu}$ or
$\epsilon_{e\tau}$ coupling in long baseline accelerator experiments for normal
and inverted mass ordering. LGtI violation is significantly enhanced in normal
ordering (NO) for $\epsilon_{e\tau}$ scenario, whereas it suppresses for
$\epsilon_{e\mu}$ scenario for T2K, NO$\nu$A, and DUNE experiment set-up. We
find that for inverted ordering (IO), in the DUNE experimental set-up above $6$
GeV, the LGtI violation can be an indication of $\epsilon_{e\tau}$ new physics
scenario.
