  Neutrino flavour oscillation is one of the primary indication of the
existence of new physics beyond standard model. The presence of small neutrino
mass is indispensable to explicate the oscillation among different flavours of
neutrino. By the addition of a right handed neutral lepton with the standard
model fermions, it is possible to generate tiny neutrino mass. Such additional
fermion may induce non-unitarity to the $3\times 3$ PMNS mixing matrix which
influences the propagation of neutrino in space-time. In this work the effect
of non-unitary mixing matrix is analyzed in neutrino oscillation in presence of
two new physics scenarios, Lorentz violation and dark non-standard interaction.
Lorentz symmetry violation mainly appears at the Planck scale, which may also
be manifested at a lower energy level. On the other hand, dark non standard
interaction arises due to the interaction of neutrino with the environmental
dark matter which contributes as a perturbative correction to the neutrino
mass. In this analysis, the comparative study of unitary and non-unitary mixing
matrix is carried out considering the scenario of Lorentz violation and dark
NSI in the context of long baseline DUNE and short baseline Daya Bay
experimental set up. The signature of dark nonstandard interaction is
observable in both DUNE and Daya Bay set up in terms of large value of neutrino
survival and oscillation probability respectively and is a possible explanation
for the excess flux observed at $\sim5$ MeV in Daya Bay experiment. The
signature of Lorentz violation is also possible to be observed in the short
baseline Daya Bay experiment only.
