Left panel: the cumulative mass functions computed at z = 6 for SD sterile neutrino models with ﹩{m}_{S}=60\,\mathrm{GeV}﹩ and ﹩{m}_{\nu }=7.1\,\mathrm{keV}﹩, for different values of the Yukawa coupling y (shown by the labels on the right) in the freeze-in limit. The shaded areas correspond to the observed number density of galaxies with ﹩{M}_{\mathrm{UV}}\leqslant -12.5﹩ within within the 1-σ, 2-σ, and 3-σ confidence levels. Right panel: the maximum value ﹩\overline{\phi }﹩ (including the theoretical uncertainties) of the predicted number density of DM halos at z = 6 for the case with ﹩{m}_{\nu }=7.1\,\mathrm{keV}﹩ as a function of the Yukawa coupling y. The upper shaded areas represent the observed number density of galaxies with ﹩{M}_{\mathrm{UV}}\leqslant -12.5﹩ within the 1-σ, 2-σ, and 3-σ confidence levels.