Model of $C_{\ell }^{\mathrm{g}\kappa }$ for three clumping cases of DM annihilation, decaying DM, and astrophysical background. The models and formatting are the same as in Fig. 2. The models assumed the redshift n(z) for z in the range of [0.1, 2.0] and energy range from 0.5 to 1000 GeV. The effect of the Fermi-LAT PSF was not considered. The blazar component shown in pink represents the unresolved blazar contribution to the astrophysical background adopted in this analysis.