This is Hartshorne, Exercise IV.4.19: Let $\mathcal{A}/\mathbb{Z} \setminus S =: T$ be an Abelian scheme. The multiplication by $n$ morphism is flat [I don't know how to show this, but I think it can be found in Katz-Mazur.], so the $n$-Torsion $\mathcal{A}[n] \to \mathcal{A}$ is also flat as it is a base change and $\mathcal{A} \to T$ also since it is flat. It is also proper and quasi-finite, and therefore finite. So we have a finite flat group scheme. Because of $(n,p) = 1$ $\mathcal{A}[n]$ is étale over $\mathbb{Z}_{(p)}$ (how to show this?). We have for $X/S$ finite étale
Consider the reduction map $\mathcal{A}[n]_\eta(\mathbf{Q}) = \mathcal{A}[n](T) \to \mathcal{A}[n]_p(\mathbf{F}_p)$ for $(n,p) = 1$, confer Liu, Chapter 10.1.3. Liu, Proposition 10.1.40(b) gives us one-point fibres of the reduction map.