There was no lording of (any) one Apostle over other Apostles. There was no Petrine "juridsiction" over the Church, because Peter was first in Antioch and it was not the center of Christendom then.
As successors to the Apostles, the bishops do not have "jurisdiction" over other bishops except as regards ecclassial structure, which is not divinely delegated, but entirely man-made.
It is true that the sacerdotal heredity in Christendom is spiritual and not biological like in Judaism, but that is also true of the Church replacing the ethnic community of Ancient Israel spiritually and not biologically
It is not necessarily "true," but it is what the Christians communities believe.
Be it as it may, the letter of Clement does contain that claim implicitly, by referring to the rod of Aaron. It correct actions taken by local authority, condemns it, and insists on correction.