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In this study,we analyze the direct-detection constraints of light dark matter in the next-to minimal supersymmetric standard model (NMSSM) with non-universal Higgs masses (NUHM);we specially focus on the correlation between higgsino asymmetry and spin-dependent (SD) cross section.We draw the following conclusions.(i) The SD cross section is proportional to the square of higgsino asymmetry in dark matter (x)01 in the NMSSM-NUHM,and hence,it is small for highly singlino-dominated dark matter.(ii) The higgsino-mass parameter μeff is smaller than approximately 335 GeV in the NMSSM-NUHM due to the current muon g-2 constraint,but our scenario with light dark matter can still be alive under current constraints including the direct detection of dark matter in the spindependent channel.(iii) With a sizeable higgsino component in the light dark matter,the higgsino asymmetry and SD cross section can also be sizeable,but dark matter relic density is always small;thus,it can escape the direct detections.(iv) Light dark matter in the h2-and Z-funnel annihilation channels with sufficient relic density can be covered by future LUX-ZEPLIN (LZ) 7-ton in SD detections.(v) The spin-independent (SI) cross section is dominated by h1-and h2-exchanging channels,which can even cancel each other in some samples,leaving an SI cross section smaller by a few orders of magnitude than that of one individual channel.