  In this paper, first we consider that the conformal vector field $\mathbf{X}$
is identical with the Reeb vector field $\varsigma$ and next, assume that
$\mathbf{X}$ is pointwise collinear with %the Reeb vector field $\varsigma$, in
both cases it is shown that the manifold $\mathbf{N}^{2m+1}$ becomes a Kenmotsu
manifold and $\mathbf{N}^{2m+1}$ is locally a warped product $\mathbf{N}'
\times_{f} \mathbf{M}^{2m}$, where $\mathbf{M}^{2m}$ is an almost K\"ahler
manifold, $\mathbf{N}'$ is an open interval with coordinate t, and $f = ce^{t}$
for some positive constant c. Beside these, we prove that if a
$(\verb"k",\boldsymbol{\mu})'$-almost Kenmotsu manifold admits a Killing vector
field $\mathbf{X}$, then either it is locally a warped product of an almost
K\"ahler manifold and an open interval or $\mathbf{X}$ is a strict
infinitesimal contact transformation. Furthermore, we also investigate
$\boldsymbol{\eta}$-Ricci-Yamabe soliton with conformal vector fields on
$(\verb"k",\boldsymbol{\mu})'$-almost Kenmotsu manifolds and finally, we
construct an example.
