  The general Sombor index of $G$ is defined as $SO_{\alpha}(G)= \sum_{uv\in
G}\left(d^2_{G}(u)+d^2_{G}(v)\right)^{\alpha}$. For $0<\alpha<1$, we have the
upper bound of $SO_{\alpha}(G)$ on unicyclic graphs with a fixed diameter, and
the extremal graph is also characterized.
