  Determination of the neutrino mass ordering (NMO) is one of the biggest
priorities in the intensity frontier of high energy particle physics. To
accomplish that goal a lot of efforts are being put together with the
atmospheric, solar, reactor, and accelerator neutrinos. In the standard
3-flavor framework, NMO is defined to be normal if $m_1<m_2<m_3$, and inverted
if $m_3<m_1<m_2$, where $m_1$, $m_2$, and $m_3$ are the masses of the three
neutrino mass eigenstates $\nu_1$, $\nu_2$, and $\nu_3$ respectively.
Interestingly, two long-baseline experiments T2K and NO$\nu$A are playing a
leading role in this direction and provide a $\sim2.4\sigma$ indication in
favor of normal ordering (NO) which we find in this work. In addition, we
examine how the situation looks like in presence of non-standard interactions
(NSI) of neutrinos with a special focus on the non-diagonal flavor changing
type $\varepsilon_{e\tau}$ and $\varepsilon_{e\mu}$. We find that the present
indication of NO in the standard 3-flavor framework gets completely vanished in
the presence of NSI of the flavor changing type involving the $e-\tau$ flavors.
