  In the context of minimal supersymmetric standard model (MSSM), we discuss
the possibility of the lightest Higgs boson with mass $M_h = 98 $ GeV to be
consistent with the $2.3\sigma$ excess observed at the LEP in the decay mode
$e^+e^- \to Zh$, with $h \to b {\bar b}$. In the same region of the MSSM
parameter space, the heavier Higgs boson $(H)$ with mass $M_H \sim 125 $ GeV is
required to be consistent with the latest data on Higgs coupling measurements
at the end of 7 + 8 TeV LHC run with $25{\rm fb}^{-1}$ of data. While scanning
the MSSM parameter space, we impose constraints coming from flavour physics,
relic density of the cold dark matter as well as direct dark matter searches.
We study the possibility of observing this light Higgs boson in vector boson
fusion process and associated production with $W/Z$ boson at the high
luminosity $(3000~{\rm fb}^{-1})$ run of the 14 TeV LHC. Our analysis shows
that this scenario can hardly be ruled out even at the high luminosity run of
the LHC. However, the precise measurement of the Higgs signal strength ratios
can play a major role to distinguish this scenario from the canonical MSSM one.
