From what I have read, the famous letter by Sherirah (Iggeret of Rabbi Sherirah Gaon) from the late 10th Century mentions two wives and offspring from each wife. I read about this in an article that provides a comprehensive survey of the Bustenai genealogy: THE POLITICAL ROLE OF SOLOMON, THE EXILARCH, C.715-759 CE (PART 1), by David H. Kelley (Foundations (2006) 2(1): 29-46). In this article, which compiles the work of prior scholars such as Moshe Gil, Felix Lazarus, Jacob Mann, and others; Kelley writes:
"Sherira (writing in the tenth century) indicated that Bustanai had two sons by a Jewish wife and three sons by a Persian wife, a royal princess who had been enslaved. The sons by the Jewish wife maintained that Bustanai had not freed and converted the Persian princess and that
her children were, therefore, illegitimate. A court found that they should be considered legitimate. Sherira says that some judges expressed doubts about the decision and he, himself, suggested that it was due to kinship between the judge and Bustanai’s part-Persian descendants. Gil summarizes all this and makes a reconstruction of the relationships. (The Gil article referred to is: Gil, Moshe (1997). The Babylonian Encounter and the Exilarchic House in the Light of Cairo
Geniza Documents and Parallel Arab Sources. In: Judaeo-Arabic Studies: Proceedings of the
Founding Conference of the Society for Judaeo-Arabic Studies (Studies in Muslim-Jewish
Relations, Vol.3), Norman Golb (editor), pp. 135-173. Amsterdam: Harwood Academic Publishers.) The Kelley article does not address the views of Avraham Grossman in Grossman, Avraham (1984). (Rashut ha-golah be-Bavel bitekufat ha-ge'onim, i.e., the Babylonian Exilarchate in the Gaonic Period). Jerusalem: The Zalman Shazar Center for the Furtherance of the Study of Jewish History, The Historical Society of Israel, which I expect may also discuss the wives and offspring of Bustenai.
I am not an expert in this area so I can only say what I have read in articles written by scholars. It does seem clear to me that there were two wives and five sons (possibly three from the Persian princess and two from the Jewish mother). Due to my only beginning to read about this history, I cannot formulate an opinion about the maternity of the various sons, nor the legitimacy of the Persian sons. For the moment I am merely looking at the GENI tree in view of the writings by these scholars and the Sherirah letter.
