  In this work, we show that Lorentz invariant theories in $1+1$ dimensions
admit new terms inspired by Very Special Relativity (VSR) theories. We have
studied the Schwinger model in VSR. We show the axial current is classically
conserved in the presence of a mass term coming from the VSR invariant terms
but without standard Lorentz invariant mass. Furthermore, it is shown that both
the vector current as well as the axial current are modified with respect to
the free case when the fermion is coupled to an external electromagnetic field
due to the nonlocal operator present in the theory. The axial anomaly is
computed, and we found the same standard topological invariant with a
modification in the coefficient.
