  In the previous article, we classified the characters associated to algebraic
points on Shimura curves of $\Gamma_0(p)$-type, and over a quadratic field we
showed that there are at most elliptic points on such a Shimura curve for every
sufficiently large prime number $p$. In this article, we get a similar result
for points over number fields of higher degree on Shimura curves of
$\Gamma_0(p)$-type.
