In this paper gravitational baryogenesis is studied by considering the simplest non-minimal matter geometry coupled f (R, T ) gravity theory where f (R, T ) = R + ζRT . Here, R represents Ricci scalar and T denote trace of the stress-energy-momentum tensor. We studied the viability of our model for different baryogenesis interactions proportional to ∂µR, ∂µT and ∂µf (R, T ). Further, we obtained baryon to entropy ratio in each case and put constraints on parameters spaces of our model. PACS numbers: 04.50.Kd; 98.80.-k; 98.80.Bp, 47.10.Fg II. OVERVIEW OF f (R, T ) GRAVITYThe late time cosmic acceleration of the universe has been explored and explained by many alternate models of classical or quantum gravity [3]. One of the most interesting theories of modified gravity is the f (R, T ) gravity. This theory is built on the coupling between matter and geometry. f (R, T ) theory can distinguish between diverse gravitational models due to its fascinating features and consistency with observations. f (R, T ) gravity models can explain the transition from matter dominated phase to the late dark energy dominated phase [25]. The gravitational Lagrangian in f (R, T ) gravity is a generic function of the Ricci scalar curvature R and the trace of stress-energy- *