Is it permissible to intend to fast a missed day (qaḍāʾ) a minute before Fajr, or must the intention be made during the night?

The intention for every obligatory fast must be formed during any part of the night, such as the fast of Ramadan, its make-up fasts, vows, and expiations. The proof for this is the saying of the Prophet, peace and blessings be upon him: "Whoever does not determine the intention to fast before Fajr has no fast." The intention is achieved merely by thinking of it. So, if you intend to fast before Fajr, even for a moment, then both the intention and the fast are valid.