Can Zakat be given to a child whose mother is from the lineage of the Prophet?

It is not permissible to give zakat (definition) to Bani Hashim (the family of the Prophet, peace be upon him) due to their honorable status, for the Prophet, peace be upon him, said: "Indeed, charity is not befitting for the family of Muhammad; it is merely the impurities of people." Lineage is determined only through the father. Therefore, if one's mother is from the Ahl al-Bayt but their father is not, they are not considered among the Ahl al-Bayt for whom charity is forbidden, and it is permissible to give them zakat.