The Prophet ﷺ did not fast any complete month of the year except Shaban, which he would join to Ramadan.
حدثنا أحمد بن حنبل حدثنا محمد بن جعفر حدثنا شعبة عن توبة العنبري عن محمد بن إبراهيم عن أبي سلمة
عن النبي ﷺ أنه لم يكن يصوم من السنة شهرا تاما إلا شعبان يصله برمضان
Reference, its isnad is sahih. Narrated by Nasai in the Book of Fasting, in the chapter on the fasting of the Prophet ﷺ, may my father and mother be sacrificed for him, and the mention of the differences among the transmitters regarding that report, hadith no. 2355, through the narration of Muhammad bin Jafar with this wording. It is also found in Musnad Ahmad, 6/311.