I have read a lot of unsourced claims online claiming that, in the course of The Book of the New Sun, Severian actually encounters things that are evidence of his own existence in the past. For example, the crypt he has taken to visiting at the beginning of the story may be his own, or he may be his own ancestor. (Dorcas is certainly his grandmother, but that does not outwardly seem to be related.) However, while there are lots of tantalizing hints that Severian is somehow connected to many more things than he yet understands, I do not recall finding any clear evidence that he is really crossing his own temporal path, if you will.
So what are the reasons for believing that some of the things young Severian encounters are really evidence left behind by an older Severian who has traveled back (or sideways, or something) in time?