This letter is devoted to investigate the matter-antimatter asymmetry through baryogenesis (and generalized gravitational baryogenesis interaction) in the realm of $f(R, A)$ theory of gravity also known as Ricci inverse gravity, where $R$ is the curvature scalar and $A$ is anti-curvature scalar. Baryogensis (baryon to entropy ratio $\frac{\eta_{_B}}{S}=\frac{\eta_{_\beta}-\eta_{\bar{\beta}}}{S}$) is a theoretical process that took place in the early history of universe producing supremacy of matter over anti-matter, where $S$ is entropy of universe and $\eta_{_\beta}(\eta_{\bar{_\beta}})$ is baryon(anti-baryon) number. In this article, we inspect the consequences of $\mathcal{C}\mathcal{P}$-violating interactions proportional to $\partial_{\nu}(R+A)$ and $\partial_{\nu}f(R+A)$. We take $f(R,A)=R+\frac{\alpha}{A}$ as specific model to analyze the phenomenon of baryogenesis and generalized gravitational baryogenesis. Our outcomes recommend that $f(R,A)$ gravity can come up consistently and significantly to the phenomenon of gravitational baryogenesis. We compare our results with latest astrophysical data of baryon to entropy ratio, which exhibits outstanding compatibility with the observational bounds.