He and Rava labelled "dardiki [Children]" by Rav Yosef, for schemes they invented for carrying items prohibited for movement on Shabbat: Shabbat 142b
A case was brought to Rav Yosef, who said, "This doesn't require examination," and Abbaye replied, "This requires extra examination!": Bava Metzia 16a
Rav Yosef chastising Abbaye for taking a brief nap: Succah 26b
Abbaye used to entertain Rabbah [perhaps Rava] by juggling 8, or perhaps 4, eggs: Succah 53a
Abbaye standing as soon as he could see the ear of Rav Yosef's donkey at a distance: Kiddushin 33a
Abbaye challenged Rabbah by quoting Rav and Shemuel; Rabbah replied, "I cite Rabbi Yochanan ben Zakkai and you reply with Rav and Shemuel?!": Beitzah 5a
Set of questions which Abbaye asked Rabbah regarding enclosures around walls, permitting drawing water within on Shabbat: Eruvin 19b-20a
Rabbah making a questionable statement before Abbaye, specifically for the purpose of testing him: Megillah 25a; Niddah 4b
Abbaye asking Rav Yosef why he hadn't taught him a specific lesson, and Rav Yosef responding that he hadn't known Abbaye was curious about. Rav Yosef asked, "Have you ever asked me something, and I haven't told it to you?": Megillah 23a
Abbaye challenged Rav Yosef on an instruction, and eventually Rav Yosef recanted, because of an anecdote wherein Rav practiced in a way which matched Abbaye's opinion: Kiddushin 39a-b
Abbaye took Purim Gifts of Food of dried and sweetened grain from Rabbah to Mari bar Mar, warning that Mari bar Mar would consider Rabbah a farmer-turned-leader. He returned with vessels containing ginger and pepper, and warned that Rabbah would say, "I sent sweet items, and he sends sharp ones!": Megillah 7b
Abbaye stated a lesson before Rav Safra, who corrected him. When Abbaye told the correction to Rav Yosef, Rav Yosef rebuked him for not asking a certain question against Rav Safra's correction: Eruvin 45b
Rabbah told Abbaye and the rest of his students to eat with him on Friday night, lest the light go out at their hosts' houses, in which case they wouldn't have Kiddush there: Pesachim 101a
The people of Kakunai asked Rav Yosef to set up arrangement merging their properties so they could transport items between them on Shabbat. Rav Yosef sent Abbaye, with the instruction, "Make sure they won't protest in the Study Hall." After several re-analyses of the situation's requirements, in which Abbaye successively required less and less of them, Abbaye said, "That's what my master meant." [Tosafot - Meaning not to demand too much of the people]: Eruvin 60a
Rav Yosef taught Abbaye a law. Abbaye asked a question about it. Rav Yosef asked what the difference was, to which Abbaye responded, "Is learning the Gemara like singing a song?!": Shabbat 106b, 113a; Eruvin 60a
Abbaye had a question against a ruling by Rabbah, but it was on a rabbinic prohibition and Rav Yosef had taught Abbaye that in such a case one should ask after the fact: Eruvin 67b-68a
Rabbah bar Rav Chanan asked Abbaye why the alley on which Abbaye and Rabbah both lived had no "merging meal" permitting transport in the area on Shabbat. Abbaye responded that it wouldn't be proper for Rabbah's honor for Rabbah to collect the meal, and Abbaye had been too busy with his learning, and the rest of the people weren't careful about it. Abbaye said he couldn't afford to donate a meal every week, so he couldn't donate a meal for joint use: Eruvin 68a
Abbaye asking Rav Yosef whether he would be allowed to sit on the part of a tree which grew in his house and extended up somewhat through a skylight: Eruvin 100a
Rav Yosef issued an order that sounded like he wanted fruit owned by an estate to be used to support an orphaned woman. Abbaye challenged him on it, and Rav Yosef explained that he only wanted fruit that was on the trees to be used: Ketuvot 50b-51a
Abbaye answering a halachic question from his sharecropper, then being corrected by his Rebbe - Rav Yosef - and running after the sharecropper for three parsah, or one parsah in sand, and not getting to him in time: Ketuvot 60b
Abbaye issued a ruling in a matter and then was corrected by Rav Yosef. He was shocked, because he had been the one to tell that law to Rav Yosef, and he took that as reinforcement of the rule of not teaching halachah before one's Rebbe: Ketuvot 60b