Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The majority of scholars of the Maliki, Shafi’e and Hambali schools of thought are of the view that if the money (wealth) of the child attains the level of the amount on which Zakah should be paid, then it has to be paid of a whole year passes on it (without being used). This is the view of Umar, Ali, Ibn Umar, Ayisha, Hussein bin Ali, and Jabir (Radiya Allahu Anhum).
A number of our righteous predecessors are of the same opinion: Ibn Sirin, Atta’, Mujahid and others.
However, the Hanafi school of thought are of a different opinion, they see that Zakah is not compulsory on the money (wealth) of a child.
The evidence of the majority of scholars is in the general meaning of the Saying of Allah: {Take Sadaqah (alms) from their wealth in order to purify them and sanctify them with it, and invoke Allâh for them. …..}[9:103], and the saying of the Prophet (Sallallahu Alaihi wa Sallam) to Mu’ad when he sent him to Yemen: “Inform them that Allah imposed on them Sadaqah which should be taken from the rich of their people and be given to the poor”. [Reported by Bukhari and Muslim, and narrated by Ibn Abbas (Radiya Allahu Anhu) and with his father.
What is relied upon, however, is the opinion of the majority of scholars; and it is the guardian of the child who should give the Zakah from the wealth of the child.
Allah knows best.