Generalised Stability of ultraproducts of finite residue rings

We study ultraproducts of finite residue rings $\mathbb{Z}\mathrm{/}n\mathbb{Z}\mathrm{╱}\mathcal{U}$ where $\mathcal{U}$ is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter $\mathcal{U}$ to determine if the resulting ultraproduct $\underset{n\in$\mathbb{N}$}{\prod}$\mathbb{Z}$/n$\mathbb{Z}$ \diagup $\mathcal{U}$$ has simple, NIP, NTP2 but not simple nor NIP, or TP2 theory, noting that all these four cases occur.