We study the potential of the LHC accelerator, and a future 33 TeV proton collider, to observe the production of a light top squark pair in association with the lightest Higgs boson (t 1t1 h 1 ), as predicted by the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We scan randomly about ten million points of the NMSSM parameter space, allowing all possible decays of the lightest top squark and lightest Higgs boson, with no assumptions about their decay rates, except for known physical constraints such as perturbative bounds, Dark matter relic density consistent with recent Planck experiment measurements, Higgs mass bounds on the next to lightest Higgs boson, h 2 , assuming it is consistent with LHC measurements for the Standard Model Higgs boson, LEP bounds for the chargino mass and Z invisible width, experimental bounds on B meson rare decays and some LHC experimental bounds on SUSY particle spectra different to the particles involved in our study. We find that for low mass top-squark, the dominating decay mode ist 1 → bχ ± 1 withχ ± 1 → Wχ 0 1 . We use three bench mark points with the highest cross sections, which naturally fall within the compressed spectra of the top squark, and make a phenomenological analysis to determine the optimal event selection that maximizes the signal significance over backgrounds. We focus on the leptonic decays of both W 's and the decay of lightest Higgs boson into b-quarks (h 1 → bb). Our results show that the high luminosity LHC will have limitations to observe the studied signal and only a proton collider with higher energy will be able to observe the SUSY scenario studied with more than three standard deviations over background. * symmetry breaking mechanism in the SM and opens up the second part, which is mandatory to establish the exact nature of the symmetry breaking mechanism and, eventually, identify the possible effects of Supersymmetry (SUSY). The available SUSY models at our disposal are many: minimal Supergravity (mSUGRA), Minimal Supersymmetric Standard Model (MSSM) [3], Next-to-MSSM (NMSSM) [4,5,6,7,8], etc. In our analysis we consider NMSSM model which solved the µ-problem of the MSSM. It is to be noted that the earlier development for the origin of the µ-term in Supertpoetial studied from Supergravity approach [9] and from the non-renormalization operators [10].The appealing of SUSY over the SM leads to an enlarged particle spectrum. As none of the SUSY particles has been discovered by any high energy collider experiment yet, SUSY must be broken. Various scenarios of the breaking mechanism have been developed in the past few decades. The top quark, the heaviest particle among the SM quark sector, having a large Yukawa coupling, has a superpartner called the top-squark, which is expected to be the lightest among all the sparticles in the enlarged squark sector, except for the gaugino sectors, like neutralinos and charginos. The light top-squark is theoretically favored from the stabilization of the Higgs potential, as well as from the longitudinal scattering ...