It could be that the analogy of papacy to Aaronic line is not a common theme in patristic literature, yet this is an example of an important letter, early pre-nicene, that carries it to a point, namely, to establish St Clement’s authority over whoever local hierarch that dismissed the priests in question.
Within his juridictional territory, of course. The point is, he was not telling other Apostolic Sees (such as the Church of Antioch or Alexnadria) how to 'behave.'
“It could be that the analogy of papacy to Aaronic line is not a common theme in patristic literature....”
Not a common theme? Its nonexistent, Alex and yet the theme of a functioning hierarchial system and the consequences of disobedience to that system is indeed a common one. But with no mention of the Bishop Rome being the top hierarch of the world.