Shortly before his death (1103), Alfasi ordained Ibn Migash as a rabbi, and - passing over his own son - also appointed him, then 26, to be his successor as Rosh Yeshiva (seminary head).
Rabbi Abraham ben David, in his work Sefer ha-Kabbalah (Book of Tradition), mentions Joseph ibn Migash, a grandfather who had the same name, as being a contemporary of Samuel haNagid, and that during the dispute between the supporters of Bulukkin and the supporters of Badis, the Berber ruler of Granada, Joseph ibn Migash had sided with Bulukkin in this dispute and fled to Askilia, to avoid punishment.
[1] It is clear that Migash was a great scholar: Maimonides in the introduction to his Mishnah commentary says "the Talmudic learning of this man amazes every one who understands his words and the depth of his speculative spirit; so that it might almost be said of him that his equal has never existed."
In Maimonides' Introduction to his Mishnah commentary, he heaps lavish praises upon Rabbi Joseph ibn Migash (Halevi), saying of him: “I have collected what I stumbled across from the glosses of my father, of blessed memory, as well as others under the name of our Rabbi Joseph Halevi, of blessed memory; and as the Lord lives, the understanding of that man in the Talmud is astounding, as anyone [can see] who observes his words and the depth of his comprehension, until I can say of him that 'there has never been any king like unto him before him' (cf.
[4] He also authored a Talmudic commentary - ḥiddushim (novellae) on tractates Baba Batra (link here) and Shevuot (included in Joseph Samuel Modiano's Uryan Telitai, Salonica 1795) - which is quoted by various Rishonim.