Told Rabbi Shimon bar Rebbe that his father Rebbe couldn't answer a question he was working on, and Rebbe ex-communicated him: Moed Katan 16a
Bar Kappara, or perhaps Rabbi Shemuel B"R Yosi, not standing before Rabbi Shimon bar Rebbe, upsetting him; he complained to his father, Rebbe: Kiddushin 33a
Rabbi Chanina said of Bar Kappara, "How courageous is one who will rule practically in accordance with his own learning!": Niddah 20a
How Bar Kappara stored his phylacteries [tefillin] when he was sleeping: Berachot 24a
Rav Hoshia learned before Bar Kappara, and then went to learn before Rabbi Chiyya. When he subsequently asked Bar Kappara a question, Bar Kappara asked what Rabbi Chiyya, "the Babylonian," would say. When Rav Hoshia couldn't answer, Bar Kappara mocked Rabbi Chiyya, calling him 'Iyya.': Keritot 8a