All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Allah The Almighty has specified eight categories entitled to receive Zakah, and some of them are: the poor and the needy. He said: "Alms are for the poor and the needy, and those employed to administer the (funds); for those whose hearts have been (recently) reconciled (to Truth); for those in bondage and in debt; in the cause of God; and for the wayfarer: (thus is it) ordained by God, and God is full of knowledge and wisdom." {At-Tawbah/60}. Moreover, He The Almighty has made Zakah a constant right for these categories. He said: " And those in whose wealth is a recognized right. For the (needy) who asks and him who is prevented (for some reason from asking)." {Al-Ma`rij,24/25}.
Therefore, none has the right to give Zakah to a category other than the aforementioned. Ziyad ibn al-Harith as-Suda'I narrated: I came to the Messenger of Allah (PBUH) and swore allegiance to him, and after telling a long story he said: Then a man came to him and said: Give me some of the sadaqah (alms). The Messenger of Allah (PBUH) said: Allah is not pleased with a Prophet's or anyone else's decision about sadaqat till He has given a decision about them Himself. He has divided those entitled to them into eight categories, so if you come within those categories, I shall give you what you desire." {Abu Dawud}.
Accordingly, it isn`t permissible for you to pay the above Sheikh from the Zakah due on your money because he doesn`t come within the categories specified in the above verse. In fact, Zakah is a constant right that must be delivered to those entitled to it; however, if the above Sheikh is poor, then he is entitled to receive Zakah.
Moreover, it is preferable for the asker to pay for his son`s education from his own wealth, not from the Zakah due on it because of the great reward that he will receive for doing so. Thawban narrated that the Messenger of Allah said: "The most virtuous of the Dinar is the Dinar spent by a man on his dependants, and the Dinar spent by a man on his beast in the Cause of Allah, and the Dinar spent by a man on his companions in the Cause of Allah." Abu Qilabah (one of the narrators) said: " He began with the dependants." Then he said: "And which man is greater in reward than a man who spends upon his dependants, having little ones by which Allah causes him to abstain (from the unlawful) and by which Allah enriches him."{At Tirmizi}. And Allah knows best.