In this paper, we introduce anti-invariant \({\xi^{\bot}}\)-Riemannian submersions from Hyperbolic β-Kenmotsu Manifolds onto Riemannian manifolds. Necessary and sufficient conditions for a special anti-invariant \({\xi^{\bot}}\)-Riemannian submersion to be totally geodesic are studied. Moreover, we obtain decomposition theorems for the total manifold of such submersions.