  We discuss both MSSM and NMSSM scenarios in which the lightest Higgs boson
with $m_h=98$~GeV is consistent with the small excess ($\sim 2.3 \sigma$)
observed at the LEP in $e^+ e^-\rightarrow Zh$, with $h \rightarrow b {\bar b}$
process and the heavier Higgs boson of mass close to 125~GeV as the observed
candidate of the SM Higgs like particle at the LHC. We show the allowed regions
in the non-decoupling Higgs zone of MSSM parameter space which are consistent
with several low energy constraints coming from heavy flavour physics, latest
experimental data on Higgs signals and lower limit on superparticle masses from
7~TeV and 8~TeV LHC run. We also implement the constraints from the relic
density of the cold dark matter as obtained from the recent PLANCK data.
Additionally, we discuss the possibility of observing the light Higgs boson of
mass 98~GeV at the 14~TeV LHC run via $pp \rightarrow V h$, with $h \rightarrow
b \bar b$ using the technique of jet substructure. Our analysis shows that at
14~TeV LHC run with 300 ${\rm fb}^{-1}$ luminosity the signal efficiency of
such a light Higgs boson is at most 2.5$\sigma$. Finally, we make a comment on
the prospect of proposed $e^+ e^-$ ILC to discover/exclude this light Higgs
boson.
