  In the present paper, we introduce the notion of $\ast$-Miao-Tam critical
equation on almost contact metric manifolds and studied on a class of almost
Kenmotsu manifold. It is shown that if the metric of a $(2n + 1)$-dimensional
$(k,\mu)'$-almost Kenmotsu manifold $(M,g)$ satisfies the $\ast$-Miao-Tam
critical equation, then the manifold $(M,g)$ is $\ast$-Ricci flat and locally
isometric to the Riemannian product of a $(n + 1)$-dimensional manifold of
constant sectional curvature $-4$ and a flat $n$-dimensional manifold. Finally,
an illustrative example is presented to support the main theorem.
