We introduce a simple scenario involving fermionic dark matter ($\ensuremath{\chi}$) and singlet scalar mediators that may account for the Galactic center GeV $\ensuremath{\gamma}$-ray excess while satisfying present direct detection constraints. $CP$ violation in the scalar potential leads to a mixing between the Standard Model Higgs boson and the scalar singlet, resulting in three scalars, ${h}_{1,2,3}$, of indefinite $CP$-transformation properties. This mixing enables $s$-wave $\ensuremath{\chi}\overline{\ensuremath{\chi}}$ annihilation into discalar states, followed by decays into four-fermion final states. The observed $\ensuremath{\gamma}$-ray spectrum can be fitted while respecting present direct detection bounds and Higgs boson properties for ${m}_{\ensuremath{\chi}}=60\ensuremath{\sim}80\text{ }\mathrm{GeV}$, and ${m}_{{h}_{3}}\ensuremath{\sim}{m}_{\ensuremath{\chi}}$. Searches for the Higgs exotic decay channel ${h}_{1}\ensuremath{\rightarrow}{h}_{3}{h}_{3}$ at the 14 TeV LHC should be able to further probe the parameter region favored by the $\ensuremath{\gamma}$-ray excess.