  This paper is devoted to the reproduction of the gravitational baryogenesis
epoch in the context of $f(R, T)$ theory of gravity, where $R$ and $T$ are
respectively the curvature scalar and the trace of the energy-momentum tensor,
respectively.
  It is assumed a minimal coupling between matter and gravity. In particular we
consider the following two models, $f(R,T) = R +\alpha T + \beta T^2$ and
$f(R,T) = R+ \mu R^2 + \lambda T$, with the assumption that the universe is
filled by dark energy and perfect fluid where the baryon to entropy ratio
during a radiation domination era is non-zero. We constrain the models with the
cosmological gravitational baryogenesis scenario, highlighting the appropriate
values of model's parameters compatible with the observation data of the
baryon-entropy ratio.
