  This paper is devoted to the study of the Higgs bundle associated with the
universal abelian variety over the good reduction of a Shimura curve of PEL
type. Due to the endomorphism structure, the Higgs bundle decomposes into the
direct sum of Higgs subbundles of rank two. They are basically divided into two
type: uniformizing type and unitary type. As the first application we obtain
the mass formula counting the number of geometric points of the degeneracy
locus in the Newton polygon stratification. We show that each Higgs subbundle
is Higgs semistable. Furthermore, for each Higgs subbundle of unitary type,
either it is strongly semistable, or its Frobenius pull-back of a suitable
power achieves the upper bound of the instability. We describe the
Simpson-Ogus-Vologodsky correspondence for the Higgs subbundles in terms of the
classical Cartier descent.
