  Nonstandard interactions (NSIs), possible subleading effects originating from
new physics beyond the Standard Model, may affect the propagation of neutrinos
and eventually contribute to measurements of neutrino oscillations. Besides
this, $ \mu-\tau $ reflection symmetry, naturally predicted by non-Abelian
discrete flavor symmetries, has been very successful in explaining the observed
leptonic mixing patterns. In this work, we study the combined effect of both.
We present an $S_4$ flavor model with $\mu-\tau$ reflection symmetry realized
in both neutrino masses and NSIs. Under this formalism, we perform a detailed
study for the upcoming neutrino experiments DUNE and T2HK. Our simulation
results show that under the $\mu-\tau $ reflection symmetry, NSI parameters are
further constrained and the mass ordering sensitivity is less affected by the
presence of NSIs.
