  In this paper we study the geometry of reduction modulo $p$ of the
Kisin-Pappas integral models for certain Shimura varieties of abelian type with
parahoric level structure. We give some direct and geometric constructions for
the EKOR strata on these Shimura varieties, using the theories of $G$-zips and
mixed characteristic local $\mathcal{G}$-Shtukas. We establish several basic
properties of these strata, including the smoothness, dimension formula, and
closure relation. Moreover, we apply our results to the study of Newton strata
and central leaves on these Shimura varieties.
