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In this paper, we investigate the implication of modular $\Gamma^{\prime}_5\simeq A^{\prime}_5$ symmetry on neutrino oscillation phenomenology in thelinear seesaw framework. In order to achieve the well defined mass structurefor the light active neutrinos as dictated by the linear seesaw mechanism, weintroduce six heavy fermion fields along with a pair of weightons to retain theholomorphic nature of the superpotential. The notable feature of modularsymmetry is that, it reduces the usage of flavon fields significantly. Inaddition, the Yukawa couplings transform non-trivially under the flavorsymmetry group and expressed in terms of the Dedekind eta functions, the $q$expansion of which renders numerical simplicity in calculations. We demonstratethat the model framework diligently accommodates all the neutrino oscillationdata. Alongside, we also investigate the effect of CP asymmetry generated fromthe decay of lightest heavy fermions to explain the observed baryon asymmetrythrough the phenomenon of leptogenesis.

Linear seesaw in $A^\prime_5$ modular symmetry with Leptogenesis