  We analyze the Higgs production via the Higgs-strahlung process
$e^{+}e^{-}\to h_{k}{\it{l}}^{+}{\it{l}}^{-}$ in an Abelian Extended
Supersymmetric SM. We work in the large Higgs trilinear coupling driven minimum
of the potential, and find that the next-to-lightest Higgs cannot be produced
by this process. Other Higgs scalars, namely the lightest and the heaviest,
have cross sections comparable to that in the pure SM. It is found that the
present model has observable differences with the other popular model, NMSSM,
in the same type of minimum.
