  In light of the observed Galactic center gamma-ray excess, we investigate a
simplified model, for which the scalar dark matter interacts with quarks
through a pseudoscalar mediator. The viable regions of the parameter space,
that can also account for the relic density and evade the current searches, are
identified, if the low-velocity dark matter annihilates through an $s$-channel
off-shell mediator mostly into $\bar{b} b$, and/or annihilates directly into
two ${\it hidden}$ on-shell mediators, which subsequently decay into the quark
pairs. These two kinds of annihilations are $s$ wave. The projected monojet
limit set by the high luminosity LHC sensitivity could constrain the favored
parameter space, where the mediator's mass is larger than the dark matter mass
by a factor of 2. We show that the projected sensitivity of 15-year Fermi-LAT
observations of dwarf spheroidal galaxies can provide a stringent constraint on
the most parameter space allowed in this model. If the on-shell mediator
channel contributes to the dark matter annihilation cross sections over 50$\%$,
this model with a lighter mediator can be probed in the projected PICO-500L
experiment.
