  We perform a global fit within the pseudo-Nambu-Goldstone dark matter (DM)
model emerging from an additional complex scalar singlet with a softly broken
global U(1) symmetry. Leading to a momentum-suppressed DM-nucleon cross section
at tree level, the model provides a natural explanation for the null results
from direct detection experiments. Our global fit combines constraints from
perturbative unitarity, DM relic abundance, Higgs invisible decay, electroweak
precision observables and latest Higgs searches at colliders. The results are
presented in both frequentist and Bayesian statistical frameworks. Furthermore,
post-processing our samples, we include the likelihood from gamma-ray
observations of $\mathit{Fermi}$-LAT dwarf spheroidal galaxies and compute the
one-loop DM-nucleon cross section. We find two favoured regions characterised
by their dominant annihilation channel: the Higgs funnel and annihilation into
Higgs pairs. Both are compatible with current $\mathit{Fermi}$-LAT
observations, and furthermore, can fit the slight excess observed in four
dwarfs in a mass range between about 30-300 GeV. While the former region is
hard to probe experimentally, the latter can partly be tested by current
observations of cosmic-ray antiprotons as well as future gamma-ray
observations.
