In the linear seesaw framework, we analyse the implications of modular $A_5^\prime$ symmetry on neutrino oscillation phenomenology. To preserve the holomorphic aspect of the superpotential, we incorporate six heavy fermion superfields along with a pair of weightons to establish the well defined mass structure for the light active neutrinos as needed by the linear seesaw mechanism. Modular symmetry has the advantage of considerably reducing the need of flavon fields. Furthermore, the Yukawa couplings alter non-trivially under the flavour symmetry group and are described in terms of Dedekind eta functions, whose $q$ expansion simplifies computations numerically. We show that the model framework meticulously accounts for all neutrino oscillation data. In addition, we investigate the implications of CP asymmetry resulting from the lightest heavy fermion decay in explaining the observed baryon asymmetry through leptogenesis.