The geometric Satake equivalence goes back to Mirkovi?--Vilonen and describes the category of perverse sheaves on the affine Grassmannian of a reductive group G over a power series ring in terms of the category of representations of its dual group. In this talk, we will consider instead the affine Grassmannian of a special parahoric model \mathcal{G} over a power, and prove the geometric Satake equivalence for their category of perverse sheaves, generalizing previous work of Richarz--Zhu from \mathbb{Q}_\ell- to \mathbb{Z}_\ell- and \mathbb{F}_\ell-coefficients. This is joint work with P. Achar, T. Richarz, and S. Riche.