Is it permissible to inhale Indian frankincense (Qust al-Hindi) smoke for the treatment of sinusitis while fasting, are the Ahadith mentioned regarding its benefits authentic, and is inhaling it permissible given that it resembles the forbidden act of smoking?

"Qust al-Hindi" (Indian Costus) is a beneficial prophetic medicine that contains seven cures.

Intentionally inhaling smoke and incense invalidates the fast according to a group of jurists, which is the view of the Hanafis and Malikis. Sheikh Ibn 'Uthaymeen, may Allah have mercy on him, also issued a fatwa to this effect. So, if one intentionally causes smoke to reach their internal cavity, their fast is broken. However, if it does not reach their throat, the fast is not broken.

It is likely that if you bring the smoke of qust close to your nose and inhale it, it will enter your throat. Therefore, if you wish to use it, it should be before Fajr (dawn) and after Maghrib (sunset).