  We investigate the energy levels of fermions within a circular graphene
quantum dot (GQD) subjected to external magnetic and Aharonov-Bohm fields.
Solving the eigenvalue equation for two distinct regions allows us to determine
the eigenspinors for the valleys $K$ and $K^\prime$. By establishing the
continuity of eigenspinors at the GQD interface, we derive an equation that
reveals the reliance of energy levels on external physical parameters. Our
observations suggest that the symmetry of energy levels hinges on the selected
physical parameters. We observe that at low magnetic fields, the energy levels
display degeneracy, which diminishes as the field strength increases,
coinciding with the convergence of energy levels toward the Landau levels. We
illustrate that the introduction of a magnetic flux into the GQD leads to the
creation of an energy gap, extending the trapping time of electrons without
perturbing the system. Conversely, the addition of gap energy widens the band
gap, disrupting the system's symmetry by introducing new energy levels.
