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The correlation between Higgs-like scalars and light dark matter is aninteresting topic, especially now that a $125 GeV$ Higgs was discovered anddark matter (DM) searches got negative results. The $95 GeV$ excess reported bythe CMS collaboration with $132 fb^{-1}$ data recently, and the DM searchresults by XENONnT and LZ collaborations motivate us to revise that. In thiswork, we study that in the GUT-scale constrained (GUTc) Next-to-MinimalSupersymmetric Model (NMSSM), where most parameters are input at the GUT scale,but with scalar and gaugino masses not unified there. In the calculation wealso consider other recent experimental constraints, such as Higgs data,Supersymmetry (SUSY) searches, DM relic density, etc. After detailed analysisand discussion, we find that: (i) The light DM can be bino- orsinglino-dominated, but can be mixed with minor components of Higgsino. (ii)Both cases can get right relic density and sizable Higgs invisible decay, byadjusting the dimensionless parameters $\lambda, \kappa$, or suitably mixingwith Higgsino. (iii) Both cases can have four funnel annihilation mechanisms,i.e., annihilating through $Z, a_1, h_2, h_1$. (iv) Samples with right relicdensity usually get weak signal of Higgs invisible decay at future leptoncollider, but the $95 GeV$ scalar can have sizable $b\bar{b}$ signal.

Light dark matter confronted with the 95 GeV diphoton excess