  The Sun is one of the most luminous $\gamma$-ray sources in the sky and
continues to challenge our understanding of its high-energy emission
mechanisms. This study provides an in-depth investigation of the solar disk
$\gamma$-ray emission, using data from the Fermi Large Area Telescope spanning
2008 August to 2022 January. We focus on $\gamma$-ray events with energies
exceeding 5 GeV, originating from 0.5$^\circ$ angular aperture centered on the
Sun, and implement stringent time cuts to minimize potential sample
contaminants. We use a helioprojection method to resolve the $\gamma$-ray
events relative to the solar rotation axes and combine statistical tests to
investigate the distribution of events over the solar disk. We found that
integrating observations over large time windows may overlook relevant
asymmetrical features, which we reveal in this work through a refined
time-dependent morphological analysis. We describe significant anisotropic
trends and confirm compelling evidence of energy-dependent asymmetry in the
solar disk $\gamma$-ray emission. Intriguingly, the asymmetric signature
coincides with the Sun's polar field flip during the cycle 24 solar maximum,
around 2014 June. Our findings suggest that the Sun's magnetic configuration
plays a significant role in shaping the resulting $\gamma$-ray signature,
highlighting a potential link between the observed anisotropies, solar cycle,
and the solar magnetic fields. These insights pose substantial challenges to
established emission models, prompting fresh perspectives on high-energy solar
astrophysics.
