<p>We study pointwise hemislant submersions as a generalization of pointwise slant submersions and hemislant submersions from cosymplectic manifolds onto Riemannian manifolds. We investigate the integrability of distributions and the geometry of totally geodesic foliations arising from the definition of these submersions. Moreover, we study the <i>ϕ</i>-pluriharmonicity of these maps and obtain some inequalities connecting the Ricci curvature with the scalar curvature, depending on whether ξ is vertical or horizontal, for pointwise hemislant submersions from cosymplectic space forms onto Riemannian manifolds.</p>