In جَاءَنِي, the yāʾ means “me” and functions as the object pronoun.
نِ is the protective nūn inserted before first-person yāʾ; it is not an additional subject or object.
Three components: جَاءَ = verb; نِ = protective nūn; ي = object pronoun. الْقَاضِي is the subject.