  The Next-to Minimal Supersymmetric Standard Model (NMSSM) with a Type-I
seesaw mechanism extends the NMSSM by three generations of right-handed
neutrino fields to generate neutrino mass. As a byproduct it renders the
lightest sneutrino as a viable DM candidate. Due to the gauge singlet nature of
the DM, its scattering with nucleon is suppressed in most cases to coincide
spontaneously with the latest XENON-1T results. Consequently, broad parameter
spaces in the Higgs sector, especially a light Higgsino mass, are resurrected
as experimentally allowed, which makes the theory well suited to explain the
long standing $b \bar{b}$ excess at LEP-II and the continuously observed
$\gamma \gamma$ excess by CMS collaboration. We show by both analytic formulas
and numerical results that the theory can naturally predict the central values
of the excesses in its broad parameter space, and the explanations are
consistent with the Higgs data of the discovered Higgs boson, $B-$physics and
DM physics measurements, the electroweak precision data as well as the LHC
search for sparticles. Part of the explanations may be tested by future DM
experiments and the SUSY search at the LHC.
