The discovery of the Higgs particle at 125 GeV has put strong constraints on minimal messenger models of gauge mediation, pushing the stop masses into the multi-TeV regime. Extensions of these models with matter-messenger mixing terms have been proposed to generate a large trilinear parameter, $A_t$, relaxing these constraints. The detailed survey of these models cite{Byakti:2013ti,Evans:2013kxa} so far considered messenger mixings with only MSSM superfields. In the present work, we extend the survey to MSSM with inverse-seesaw mechanism. The neutrino-sneutrino corrections to the Higgs mass in the inverse seesaw model are not significant in the minimal gauge mediation model, unless one considers messenger-matter interaction terms. We classify all possible models with messenger-matter interactions and perform thorough numerical analysis to find out the promising models. We found that out of the 17 possible models 9 of them can lead to Higgs mass within the observed value without raising the sfermion masses significantly. The successful models have stop masses $sim $1.5 TeV with small or negligible mixing and yet a light CP even Higgs at 125 GeV.
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