  For the newly discovered $W$-boson mass anomaly, one of the simplest dark
matter (DM) models that can account for the anomaly without violating other
astrophysical/experimental constraints is the inert two Higgs doublet model, in
which the DM mass ($m_{S}$) is found to be within $\sim 54-74$ GeV. In this
model, the annihilation of DM via $SS\to b\bar{b}$ and $SS\to WW^{*}$ would
produce antiprotons and gamma rays, and may account for the excesses identified
previously in both particles. Motivated by this, we re-analyze the AMS-02
antiproton and Fermi-LAT Galactic center gamma-ray data. For the antiproton
analysis, the novel treatment is the inclusion of the charge-sign-dependent
three-dimensional solar modulation model as constrained by the time-dependent
proton data. We find that the excess of antiprotons is more distinct than
previous results based on the force-field solar modulation model. The
interpretation of this excess as the annihilation of $SS\to WW^{*}$ ($SS\to
b\bar{b}$) requires a DM mass of $\sim 40-80$ ($40-60$) GeV and a
velocity-averaged cross section of $O(10^{-26})~{\rm cm^3~s^{-1}}$. As for the
$\gamma$-ray data analysis, besides adopting the widely-used spatial template
fitting, we employ an orthogonal approach with a data-driven spectral template
analysis. The fitting to the GeV $\gamma$-ray excess yields DM model parameters
overlapped with those to fit the antiproton excess via the $WW^{*}$ channel.
The consistency of the DM particle properties required to account for the
$W$-boson mass anomaly, the GeV antiproton excess, and the GeV $\gamma$-ray
excess suggest a common origin of them.
