What is the source and manner by which the Household of the Messenger of Allah and their descendants obtain their right to the Khums mentioned in the Qur'an, given that Zakat and Sadaqa are impermissible for them?

Charity (sadaqah) is forbidden for the Ahl al-Bayt (the Prophet's household), and they are entitled to the Khums (one-fifth), based on the Almighty's saying: "What Allah has bestowed upon His Messenger from the people of the towns, it is for Allah and for the Messenger and for [his] near relatives and orphans and the [entirely] needy and the traveler." (Quran 59:7), and His saying: "And know that whatever you take as war booty, then indeed for Allah is one fifth of it and for the Messenger and for [his] near relatives and the orphans and the needy and the traveler." (Quran 8:41). The Ahl al-Bayt must be given their sufficiency from the public treasury (Bayt al-Mal). Scholars have differed on the permissibility of giving them from zakat if their right from the public treasury is withheld. Ibn Taymiyyah chose permissibility, but it is more virtuous for a Hashemite to abstain from zakat and be patient. Rulers should attend to the Ahl al-Bayt and grant them their rights from the Muslims' public treasury.