  We extend the colored Zee-Babu model with a gauged $U(1)_{B-L}$ symmetry and
a scalar singlet dark matter (DM) candidate $S$. The spontaneous breaking of
$U(1)_{B-L}$ leaves a residual $Z_2$ symmetry that stabilizes the DM and
generates tiny neutrino mass at the two-loop level with the color seesaw
mechanism. After investigating dark matter and flavor phenomenology of this
model systematically, we further focus on its imprint on two of cosmic-ray
anomalies: the Fermi-LAT gamma-ray excess at the Galactic Center (GCE) and the
PeV ultra-high energy (UHE) neutrino events at the IceCube. We found that the
Fermi-LAT GCE spectrum can be well fitted by DM annihilation into a pair of
on-shell singlet Higgs mediators while being compatible with the constraints
from relic density, direct detections as well as dwarf spheroidal galaxies in
the Milky Way. Although the UHE neutrino events at the IceCube could be
accounted for by resonance production of a TeV-scale leptoquark, the relevant
Yukawa couplings have been severely limited by current low energy flavor
experiments. We then derive the IceCube limits on the Yukawa couplings by
employing its latest 6-year data.
