Should a person who wants to fast for the holy nights fast on the day of that night or on the next day?

In religious terms, a day finishes with sunset and a new day begins. Night comes before daytime (Qurtubi, al-Jami’, XIV, 15). Therefore, because the month of Ramadan begins with the sunset on the last day of Shaban, tarawih prayer is performed that night, and because Shawwal begins on the last day of Ramadan with sunset, tarawih prayer is not performed that night. Friday begins when the sun sets on Thursday and continues till the evening on Friday. For example, when one says “the first Friday night of Rajab,” we should know that it is the first night that connects Thursday to Friday (the time from sunset to fajr). Likewise, “the 15th night of Shaban” is the night that connects the 14th day to the 15th day of the month, and “the eid night” is the night that connects the day of arafah to eid day.

In this regard, the true time to fast nafl for the holy nights is the day following the night, but one also may fast by adding the former day.

Source: Presidency Of Religious Affairs The Turkey, High Board of Religious Affairs FATWAS

Is There Any Religious Obligation About Fasting In The Days Of The Holy Nights?