We give a new cyclic sieving phenomenon for semistandard Young tableaux $SSYT(λ,μ)$ of shape $λ=(m,n^b)$ and content $μ$, a $(b+2)$-tuple. We prove that $(SSYT(λ,μ),\langle \partial^{b+2} \rangle, f(q))$ exhibits the cyclic sieving phenomenon, where $\partial$ is the jeu de taquin promotion operator and $f(q)$ is a modified Kostka-Foulkes polynomial $\widetilde{K}_{λ,μ}(q)$, up to a power of $q$.