I had always assumed that R' Yehoshua Ben Levi was an Amorah. However, we know he is quoted in the mishnah in Avos (Perek 6 Mishnah 2. Which is really a braisa, not a mishnah, but still a Tannaic source).
Are there any discussions about this (either way): if R' Yehoshua Ben Levi was a Tanna or an Amorah?
The Tzla'ch in Berachot 26b says the גמרא can't ask on Rebbe Yehoshua ben Levi from a ברייתא because he lived at the end of the Tannayic era and, therefore can argue on a ברייתא
The Rambam mentions him in the הקדמה to משניות in his list of people mentioned in the משנה as "someone mentioned but not for his views in אסור והיתר".
R' Sherira Gaon lists him as the same generation as Rav and Shmuel, but does not list him as one of the people how is both a Tanna and an Amora. it would seem that R' Sherira hold that he is not a Tanna.
I found the following today:
Rashi in Niddah Daf 18b says that R' Yehoshua Ben Levi was an Amorah,
שמעתתא. ר' יהושע בן לוי אמורא הוא
The last Mishnah in Uktzin - perek 3 mishnah 12 - starts with a quotation from R' Yehoshua Ben Levi. Tosafos Yom Tov there says that according to the Rambam he is a Tanna. However, at the end of the Masechto, Tosafos Yom Tov disagrees and gives a reason why Rabeinu Hakodosh, the copiler of the Mishnah, put in this saying of R' Yehoshua Ben Levi, even though he was not a Tanna. London Shevat 5776
Rav Yitzchak Yosef (Ein Yitzchak vol. 1 page 274) lists it as a Machaloket Rashi and the Rambam if he was an Amora who could argue on Tannaim (like Rav and Rav Chiya) or an actual Tanna, respectively.
In סדר הדורות הקצר on p.71 it has the following listing;
Rabbi Yehoshua ben Levi
A student of Rebbi, from the first generation of Israeli Amoraim. He was also of the students of Rabbi Elazar HaKafar and Rabbi Yehuda ben Pediah - he gave over many (ideas/teachings) in the name of Bar Kafra. He is regarded as one of the great sages of Aggadah. His students include: Rabbi Yochanan, Rabbi Elazar, Rabbi Chiya bar Abbah. He merited to enter into Gan Eden alive (one of only 10 who merited this), he frequently saw the revelation of Eliyahu HaNavi and spoke with Moshiach ben David
