Algebraic points on Shimura curves of $\Gamma_0(p)$-type

We classify the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over number fields (not only quadratic fields but also fields of higher degree) we show that there are few points on such a Shimura curve for every sufficiently large prime number $p$. This is an analogue of the study of rational points or points over quadratic fields on the modular curve $X_0(p)$ by Mazur and Momose.