We discuss both the minimal supersymmetric Standard Model (MSSM) and next to MSSM scenarios in which the lightest Higgs boson with mh=98 GeV is consistent with the small excess (∼2.3σ) observed at the LEP in e+e-→Zh, with the h→bb̄ 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 nondecoupling Higgs zone of MSSM parameter space which are consistent with several low energy constraints coming from heavy flavor physics, the latest experimental data on Higgs signals, and the lower limit on superparticle masses from 7 and 8 TeV LHC runs. 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→Vh, with h→bb̄ using the technique of jet substructure. Our analysis shows that at a 14 TeV LHC run with 300 fb-1 luminosity the signal efficiency of such a light Higgs boson is at most 2.5σ. Finally, we make a comment on the prospect of the proposed e+e- International Linear Collider to discover/exclude this light Higgs boson. © 2013 American Physical Society.