What is the role of a cardinal-bishop in an archdiocese?

If I'm from a Catholic Diocese that has a bishop who is its ordinary bishop, we're sort of a member under the wing of a neighboring archdiocese with an archbishop (this makes sense). But the archdiocese is adjacent to another archdiocese whose head is a cardinal. Does this cardinal have some power/jurisdiction/authority over the archdiocese/diocese I am a member of?