It is narrated from Usama ibn Zayd (رضي الله عنه) that he asked the Messenger of Allah (ﷺ):
“I have never seen you offer fast in a month as you do in Sha'ban.”
To which, the Prophet (ﷺ) replied:
“It is a month between Rajab and Ramadan that people disregard. In that month deeds are presented to the Lord of the Worlds, so I like my deeds to be presented while I am fasting.” (Nasai)
Aishah (رضي الله عنها) reported:
The Messenger of Allah (ﷺ) did not observe voluntary Saum (fasting) so frequently during any other month as he did during Shaban. He observed Saum all of the month of Shaban.
And in another narration: He (ﷺ) observed Saum during the whole month of Shaban except a few days.
[Al-Bukhari & Muslim].
Clarifying the Doubt of Fasting the Second half of Sha'ban
Imaam Al-Nawawi (رحمه الله) said: