  The Co-intercalated NbS$_2$ (Co$_{1/3}$NbS$_2$) compound exhibits large
anomalous Hall conductance, likely due to the non-coplanar magnetic ordering of
Co spins. In this work, we study the relation between this novel magnetism and
the correlated electronic structure of Co$_{1/3}$NbS$_2$ by adopting dynamical
mean field theory (DMFT) to treat the correlation effect of Co $d$ orbitals. We
find that the hole doping of Co$_{1/3}$NbS$_2$ can tune the size of the Nb hole
pocket at the DMFT Fermi surface, producing features consistent with those
observed in angle resolved photoemission spectra [Phys. Rev. B 105, L121102
(2022)]. We also compute the momentum-resolved spin susceptibility, and
correlate it with the Fermi surface shape. We find that the magnetic ordering
wavevector of Co$_{1/3}$NbS$_2$ obtained from the peak in spin susceptibility
agrees with the one observed experimentally by neutron scattering; it is
compatible with commensurate non-coplanar $3q$ spin structure. We also discuss
how results change if some other than Co transition metal intercalations are
used.
