  The only allowed Higgs superpotential term at stringy tree level in the
string derived Singlet Extensions of the Minimal Supersymmetric Standard Model
(SEMSSM) is h S H_d H_u, which leads to an additional global U(1) symmetry in
the Higgs potential. We propose the string inspired SEMSSM where the global
U(1) symmetry is broken by the additional superpotential terms or supersymmetry
breaking soft terms that can be obtained naturally due to the instanton effects
or anomalous U(1)_A gauge symmetry. In these models, we can solve the \mu
problem and the fine-tuning problem for the lightest CP-even Higgs boson mass
in the MSSM, generate the baryon asymmetry via electroweak baryogenesis, and
predict the new Higgs physics which can be tested at the LHC and ILC.
