  Based on the NilHecke algebra $\mathsf{NH}_n$, the odd NilHecke algebra
developed by Ellis, Khovanov and Lauda and Kang, Kashiwara and Tsuchioka's
quiver Hecke superalgebra, we develop the Clifford Hecke superalgebra
$\mathsf{NH}\mathfrak{C}_n$ as another super-algebraic analogue of
$\mathsf{NH}_n$. We show that there is a notion of symmetric polynomials
fitting in this picture, and we prove that these are generated by an
appropriate analogue of elementary symmetric polynomials, whose properties we
shall discuss in this text.
