Phenomenological Aspects of  \(S_3\) Modular Symmetry on Linear Seesaw with Leptogenesis

The uniqueness of this work is that it employs the Linear Seesaw mechanism in SUSY to create a model that explains neutrino oscillation data under \(S_3\) modular symmetry. The Standard Model (SM) is supplemented by three RH neutrinos ( \(N_{R_i}\) ) and three Sterile neutrinos ( \(S_{L_i}\) ), as well as one weighton that eliminates unnecessary components in the superpotential and maintains the model consistent.