  We investigate supercurrent interference patterns measured as a function of
magnetic field in ballistic graphene Josephson junctions. At high doping, the
expected $\Phi_{0}$-periodic "Fraunhofer" pattern is observed, indicating a
uniform current distribution. Close to the Dirac point, we find anomalous
interference patterns with an apparent 2$\Phi_{0}$ periodicity, similar to that
predicted for topological Andreev bound states carrying a charge of $e$ instead
of $2e$. This feature persists with increasing temperature, ruling out a
non-sinusoidal current-phase relationship. It also persists in junctions in
which sharp vacuum edges are eliminated. Our results indicate that the observed
behavior may originate from an intrinsic property of ballistic graphene
Josephson junctions, though the exact mechanism remains unclear.
