All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In the Quran, Allah designated eight categories of people eligible to receive Zakah : "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}. In addition, Narrated Ziyad ibn al-Harith as-Suda'i:
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 Dawoud}.
Building or maintaining schools doesn`t fall into any of the eight categories stated in the above verse. Therefore, it isn`t permissible to pay Zakah money to cover the expenses of building or maintaining schools. However, it is permissible to collect voluntary charities to this end or guide people to donate to the educational Waqf (Endowment), for this is encouraged by Resolution No.(6/2018) of the Jordan Iftaa` Council. This Resolution states: "Giving donations to improve the educational process and endowing wealth in favor of the educational Waqf initiative is required by Sharia." However, this is taking into account that the donation doesn`t contradict with the instructions of the Jordan Ministry of Education. And Allah the Almighty knows best.