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We discuss both MSSM and NMSSM scenarios in which the lightest Higgs bosonwith $m_h=98$~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 observedcandidate of the SM Higgs like particle at the LHC. We show the allowed regionsin the non-decoupling Higgs zone of MSSM parameter space which are consistentwith several low energy constraints coming from heavy flavour physics, latestexperimental data on Higgs signals and lower limit on superparticle masses from7~TeV and 8~TeV LHC run. We also implement the constraints from the relicdensity of the cold dark matter as obtained from the recent PLANCK data.Additionally, we discuss the possibility of observing the light Higgs boson ofmass 98~GeV at the 14~TeV LHC run via $pp \rightarrow V h$, with $h \rightarrowb \bar b$ using the technique of jet substructure. Our analysis shows that at14~TeV LHC run with 300 ${\rm fb}^{-1}$ luminosity the signal efficiency ofsuch a light Higgs boson is at most 2.5$\sigma$. Finally, we make a comment onthe prospect of proposed $e^+ e^-$ ILC to discover/exclude this light Higgsboson.

Implications of 98 GeV and 125 GeV Higgs scenario in non-decoupling SUSY with updated ATLAS, CMS and PLANCK data