  This paper aims to recreate the gravitational baryogenesis epoch in the
framework of the $f(R,L_m)$ theory of gravity, where $R$ and $L_m$ are the
curvature scalar and the matter Langragian, respectively. In particular, we
examine the model, $f(R,L_m) = \frac{R}{2} + L_m ^{\alpha} + \zeta$, under the
supposition that the universe is saturated with dark energy and perfect fluid,
with a non-zero baryon to entropy ratio during a radiation dominance era. We
confine the model with the gravitational baryogenesis scenario, emphasizing the
appropriate values of model parameters compatible with the baryon-to-entropy
ratio observation data. Our study found that $f(R,L_m)$ gravity can
considerably and steadily make a contribution to the phenomenon of
gravitational baryogenesis.
