  We probe quantum oscillations in nodal line semimetals (NLSM) by considering
a NLSM continuum model under strong magnetic field and report the
characteristics of the Landau level spectra and the fluctuations in the Fermi
level as the field in a direction perpendicular to the nodal plane is varied
through. Based on the results on parallel magnetization, we demonstrate the
growth of quantum oscillation with field strength as well as its constancy in
period when plotted against 1/B. We find that the density of states which show
series of peaks in succession, witness bifurcation of those peaks due to Zeeman
effect. For field normal to nodal plane, such bifurcations are discernible only
if the electron effective mass is considerably smaller than its free value,
which usually happens in these systems. Though a reduced effective mass $m^*$
causes the Zeeman splitting to become small compared to Landau level spacing,
experimental results indicate a manyfold increase in the Lande $g$ factor which
again amplifies the Zeeman contribution. We also consider magnetic field in the
nodal plane for which the density of state peaks do not repeat periodically
with energy anymore. The spectra become more spread out and the Zeeman
splittings become less prominent. We find the low energy topological regime,
that appears with such in-plane field set up, to shrink further with reduced
$m^*$ values. However, such topological regime can be stretched out in case
there are smaller Fermi velocities for electrons in the direction normal to the
nodal plane.
