  In the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM),
singlet particles may form a secluded sector of dark matter (DM), in which
Singlino-like DM could achieve the observed relic abundance through various
channels such as $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to h_s h_s, A_s A_s, h_s
A_s$, where $h_s$ and $A_s$ represent singlet-dominated CP-even and CP-odd
Higgs bosons. We provide analytical formulas for both the spin-independent and
spin-dependent cross sections of Singlino DM scattering with nucleons,
illustrating their dependence on the model's parameters in a clear manner. We
also present analytic expressions for the annihilation cross sections of these
three important channels. Based on these preparations, we conducted Bayesian
analyses of the GNMSSM and concluded that the theory significantly favored
Singlino-dominated DM over Bino-like DM across a much broader range of
parameters. The combined results from our numerical analyses and the formulas
distinctly highlight crucial aspects of DM physics within the GNMSSM.
