The Messenger of Allah ﷺ used to fast the first nine days of Dhul-Hijjah, the day of Ashura, and three days of every month, the first Monday of the month and two Thursdays.
كان رسول الله ﷺ يصوم تسع ذي الحجة، ويوم عاشوراء، وثلاثة أيام من كل شهر: أول اثنين من الشهر والخميسين.
Abu Dawud (2437), Nasai (2417), and Ahmad (26468) all narrated it via Abu Awana, from Hurr bin Sabbah, from Hunayda bin Khalid, from his wife, from one of the wives of the Prophet ﷺ. This chain is sahih. I could not find the name of Hunayda's wife, except that Hafiz mentioned in Taqrib, in the section on unnamed narrators, that she was a Companion.Nasai (2415) also narrated it through another route, from Zuhayr, from Hurr bin Sabbah, who said, "I heard Hunayda al-Khuzai say, I entered upon the Mother of the Believers and heard her say, 'The Messenger of Allah ﷺ used to fast three days of every month, the first Monday of the month, then Thursday, then the following Thursday.'" Here he omitted Hunayda's wife. This chain is also sahih, for Hunayda first heard it from his wife, who related it from the Mother of the Believers, and then he himself entered upon her and heard it from her directly. This is something well known in the science of hadith.This hadith has been narrated in other forms, some of which are not sound. Whoever judged it to be inconsistent was mistaken, for what is sound is not harmed by what is not sound, and one should not resort to a judgment of inconsistency unless it proves impossible to reconcile the various narrations.As for what was narrated from Hafsa, who said, "The Messenger of Allah ﷺ used to fast three days of the month, Monday and Thursday, and the Monday of the following week," it contains a narrator who is deemed acceptable. Abu Dawud (2451), Nasai (2366), and Ahmad (26460, 26463) all narrated it through Hammad, from Asim bin Bahdala, from Sawa al-Khuzai, from Hafsa, and he related it.Two others narrated from Sawa al-Khuzai, namely Musayab bin Rafi and Mabad bin Khalid. Ibn Hibban mentioned him in Thiqat, as Mizzi stated, except that his biographical entry was dropped from the printed edition, since the editor of Tahzib Kamal attributed it to the manuscript. That is why Hafiz said in Taqrib, "Acceptable," meaning when corroborated.I did not find anyone who corroborated him. In fact, it contradicts the sahih hadith stating that he ﷺ used to fast the first Monday of the month and the two Thursdays. This may be attributable to Asim bin Bahdala, for scholars have criticized his memory, and because he was inconsistent in narrating it. At one time he narrated it from Sawa, from Hafsa, at another time from him, from Umm Salama, as with Nasai (2365), and at another time from him, from Musayab, from Hafsa, where it states, "He ﷺ used to fast Monday and the two Thursdays," without mentioning Sawa. Imam Ahmad (26461) and Nasai narrated it likewise. Musayab here is Musayab bin Rafi, who did not hear from Hafsa.This hadith has other chains of transmission, and it appears that inconsistency occurred in both the chain and the text, since they all revolve around Asim bin Bahdala, of whom Bazzar said, "He was not known for a strong memory," and Daraqutni said, "There is something questionable about his memory." A narrator like him cannot be relied upon when he contradicts others.