The Bavli often says "אמר פלוני אמר פלוני" ("So-and-so said that So-and-so said…") or "אמר פלוני משמיה דפלוני" ("So-and-so said in the name of So-and-so…") or "כי אתא פלוני אמר פלוני" ("When So-and-so arrived, [he said that] So-and-so had said…"). Is the person being quoted ever a student of the quoting person's?
(Disclaimer: This was developed based on the below sources, not based on any special Bekius that I have in Shas...)
Tosfos to Pesachim 100a seem to think that this is an impossibility, based on their comment that the correct Girsa cannot be Rabbi Yochanan quoting Rabbi Avahu, since the latter was the former's talmid:
ה"ג והאמר ר' ירמיה א"ר יוחנן ואיתימא רבי אבהו א"ר יוסי בר ר' חנינא ולא גרס רבי יוחנן א"ר אבהו דרבי אבהו תלמידיה דר' יוחנן הוה:
The concept of a Rabbi quoting his student in the Talmud is discussed at length in this introduction to Seder Hadoros. He gives a number of examples found in the Bavli and Yerushalmi (despite his rejecting of those Girsaos), see there for details, although one of them is the Tosfos's rejected Girsa in Pesachim that we quoted above. A source that he brings that we do have in our Girsa would be Pesachim 102b:
אמר רב הונא אמר רב ששת אין אומרים שתי קדושות על כוס אחד
Based on other gemaras (see the link to the Seder Hadoros intro), and noted in the handy chart here, Rav Sheshes was a Talmid of Rav Huna.
See also here (and quoted sources) for a detailed discussion of the term אמר רבי פלוני אמר רבי פלוני in general.