In this analysis we explore the phenomenological constraints of models with non-holomorphic soft SUSY breaking terms in a beyond the MSSM scenario having identical particle content. The model referred as NHSSM shows various promising features like the possibility of a strong reduction in electroweak fine-tuning even for a scenario of a heavy higgsino type of LSP, a fact that is unavailable in pMSSM models. The other important aspect is satisfying the muon $g-2$ data even for a small $tanbeta$ via a small value of coupling $A_mu$ associated with the tri-linear non-holomorphic soft term. Thus, a large SUSY contribution to muon $g-2$ is possible even for a significantly large smuon mass $m_{tilde {mu_1}}$. The Higgs mass radiative corrections are contributed by both the holomorphic and non-holomorphic trilinear soft parameters $A_t$ and $A_t$, thus diluting the requirement to have a larger $A_t$ to satisfy the Higgs mass data. The model also provides with valid parameter space satisfying the constraint of $B rightarrow X_s +gamma$ for large values of $tanbeta$, a scenario unfavourable in pMSSM.
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