Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with giving zakah to poor students as long as they are poor and need the zakah to continue their studies.
In his response to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
Zakah is the third pillar of Islam. We read in the Quran:
{And establish prayer and give zakah and bow with those who bow [in worship and obedience].} (Al-Baqarah 2:43)
Prophet Muhammad (peace be upon him) said: Islam is built on five pillars:
1- To testify that none has the right to be worshipped but Allah and Muhammad is Allah’s Messenger.
2- To offer the (compulsory congregational) prayers dutifully and perfectly.
3- To pay Zakah (i.e. obligatory charity.
4- To perform Hajj. (i.e. Pilgrimage to Makkah)
5- To observe fast during the month of Ramadan. (Al-Bukhari)
About the recipients of zakah, we read in the Quran:
{Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler – an obligation [imposed] by Allah . And Allah is Knowing and Wise.} (At-Tawbah 9:60)
Based on this verse, there is nothing wrong with giving zakah to poor students as long as they are poor and need the zakah to continue their studies.
Almighty Allah knows best.