  Holomorphic Cliffordian functions of order $k$ are functions in the kernel of
the differential operator $\overline{\partial}\Delta^k$. When
$\overline{\partial}\Delta^k$ is applied to functions defined on the paravector
space of some Clifford Algebra $\mathbb{R}_m$ with an odd number of imaginary
units, the Fueter-Sce construction establish a critical index $k=\frac{m-1}{2}$
(sometimes called Fueter-Sce exponent) for which the class of slice regular
functions is contained in the one of holomorphic Cliffordian functions of order
$\frac{m-1}{2}$. In this paper we analyze the case $k<\frac{m-1}{2}$ and we
find that the polynomials of degree at most $2k$ are the only slice regular
holomorphic Cliffordian functions of order $k$.
