  In Very Special Relativity (VSR), the neutrino mass term is coupled with the
VSR preferred axis, and hence Lorentz violating in nature. Beyond standard
model physics predicts neutrino magnetic moment which is linearly proportional
to the mass eigenstates of the neutrinos. We report an additive kinematic phase
in the neutrino flavor oscillation due to the neutrino magnetic moment in the
VSR framework. This phase is proportional to the coupling between the VSR
preferred axis with the external magnetic field as well as the spin of the
neutrino. Furthermore, we predict time variation in the neutrino oscillation
with a period of one sidereal day.
