All perfect praise be to Allah, The Lord of The Worlds; and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Providing for one`s sister is a good deed and a noble act that only comes from a generous person who seeks reward from Almighty Allah. However, according to our school of thought, Shafie, this act isn't an obligation, because one is only obliged to provide for ascendants, descendants and wife.
In this regard, Al-Kahteeb As-Shrbini (May Allah have mercy on his soul) said (What means): " it is an obligation upon every Muslim to cover the expenses of ascendants, descendants and wife. As for other relatives (brother, sister, uncle and aunt), they aren't included ." [Mughni Al-Muhtaj vol.5, pp.184].
Therefore, a brother is permitted to cover the expenses of his poor sister and give her money as Zakah if she doesn`t receive enough support to pursue her studies, she is an overeager student and her field of study doesn`t involve any violations of Sharia.
Moreover, the sister is more entitled, than anyone else, to receive Zakah from her brother, because the Prophet (PBUH) said (What means): "Giving charity to a poor person is charity, and (giving) to a relative is two things, charity and upholding the ties of kinship." [At-Trmithi]. And Allah, The Almighty Knows Best.