  Neutrinos, due to their weakly interacting nature, provide us with a unique
opportunity to test foundations of quantum mechanics over macroscopic
distances. There has been considerable theoretical and experimental interest in
examining the extent of violation of Leggett-Garg inequalities (LGI) in the
context of neutrino flavour oscillations. While it is established that neutrino
oscillations occur due to mass and mixing among the three generations of
neutrinos, sub-dominant effects due to physics beyond the Standard Model (SM)
are not yet ruled out. As we are entering the precision era in neutrino
physics, it is possible that some of these effects may leave an imprint on
data. Thus, it is worthwhile to investigate different physics scenarios beyond
the SM and study their impact on oscillation probabilities. In the present
work, we invoke damping effects (including decoherence and decay) on
oscillation probabilities and study their implications on the LGI.
