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We study the features of the additional Higgs bosons in the Next-to-MinimalSupersymmetric Standard Model where the lightest beyond Standard Model Higgsboson does not dominantly couple to up-type quarks. The new state is dominantlysinglet-like while it can also accommodate a small down-type Higgs component.The gluon-gluon fusion cannot be adequate enough for such a Higgs production.We show that the vector-boson fusion may become the leading productionmechanism to probe this new scalar at the LHC. Using the existing 13 TeV LHCdata for an integrated luminosity $36.1~fb^{-1}$, we show the LHC constraintson the parameter space. Finally, we also study the reach of the planned highluminosity LHC (${\mathcal L}=3~{\rm ab}^{-1}$ at $\sqrt s=$~14 TeV) and theproposed high energy upgrade of the LHC (${\mathcal L}=15~{\rm ab}^{-1}$ at$\sqrt s=$~27 TeV) to probe this singlet-like Higgs scalar.

Dominant production of heavier Higgs bosons through vector boson fusion in NMSSM