  In this letter we study some variant forms of gravitational baryogenesis by
using higher order terms containing the partial derivative of the Gauss-Bonnet
scalar coupled to the baryonic current. This scenario extends the well known
theory that uses a similar coupling between the Ricci scalar and the baryonic
current. One appealing feature of the scenario we study is that the predicted
baryon asymmetry during a radiation domination era is non-zero. We calculate
the baryon to entropy ratio for the Gauss-Bonnet term and by using the
observational constraints we investigate which are the allowed forms of the
$R+F(\mathcal{G})$ gravity controlling the evolution. Also we briefly discuss
some alternative higher order terms that can generate a non-zero baryon
asymmetry, even in the conformal invariance limit.
