Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\text{Q}$

Associated to an open subgroup $G$ of ${\text{GL}}_2(\text{Zhat})$ satisfying conditions $-I\in G$ and $\det (G)⊊(\text{Zhat}{)}^{\times }$ there is a modular curve $X_G$ which is a smooth compact curve defined over an extension of $\text{Q}\mathrm{.}$ In this article, we give a complete list of all such prime power level genus $0$ modular curves with a point.