  This study reanalyzes the detection prospects of dark matter (DM)
annihilation signals in the Galactic Center, focusing on velocity-dependent
dynamics within a spike density near the supermassive black hole
(Sgr~A$^{\star}$). We investigate three annihilation processes -- $p$-wave,
resonance, and forbidden annihilation -- under semi-relativistic velocities,
leveraging gamma-ray data from Fermi and DAMPE telescopes. Our analysis
integrates a fermionic DM model with an electroweak axion-like particle (ALP)
portal, exploring annihilation into two or four photons. Employing a
comprehensive six-dimensional integration, we precisely calculate DM-induced
gamma-ray fluxes near Sgr~A$^{\star}$, incorporating velocity and positional
dependencies in the annihilation cross-section and photon yield spectra. Our
findings highlight scenarios of resonance and forbidden annihilation, where the
larger ALP-DM-DM coupling constant $C_{a\chi\chi}$ can affect spike density,
potentially yielding detectable gamma-ray line spectra within Fermi and DAMPE
energy resolution. We set upper limits for $C_{a\chi\chi}$ across these
scenarios, offering insights into the detectability and spectral
characteristics of DM annihilation signals from the Galactic Center.
