End of last season (my first as a referee), big game in this particular division, the loser of which would almost certainly be relegated.
Home manager comes upto me 2 mins before kick off and says that he recognises 3 opposition players that aren't signed on (shows me on full time to prove it) and he doesn't think they should be allowed to play. I approached the away manager for clarification and he said that they were in dispute with the League Secretary regarding this and offered to show me emails proving this. I just said that we will play the gan3 as this is beyond my jurisdiction and I'll report this to the league, which I did.
The away team won a tight game,in which one of the disputed players scored 2 goals so you can imagine the comments after the game. To my knowledge the away manager was telling the truth and their eligibility was proven.
The away team assistant manager disagreed with my decision not to award a penalty in the 2nd half, to the extent that he was asked to leave (I learnt some new words that day!).
My point being that player eligibility issues and my jurisdiction wasn't clear to me (never encountered such a problem) so I went with what I thought was sensible (and I think I was correct). If it happened again I would do exactly the same, play the game and report the names of the players concerned afterwards to the league. Would be interesting to know if anyone would do anything differently as despite it seemingly being the sensible course of action, the incident still remains in your mind throughout the evening
I would have been on a similar track but wouldn't have bothered to be shown a list of players names on fulltime. It would mean nothing to me unless they showed me their driving licence at the same time. I always tell them to take it up with the league, I'm there to referee not perform a register. Maybe at a push, I'd mention it in passing to the opposition manager but again, not look for proof. Once aware, they are doing it at their own risk