The three schools of jurisprudence other than the Hanafi school state that Zakat should be paid on qualifying wealth owned by the orphan, child and the insane.
These three schools of jurisprudence consider the ownership of wealth reaching the Nisab as the driving factor behind the Zakat obligation. Furthermore, the child, insane and orphan’s wealth will also benefit from the purification of wealth due to the payment of Zakat. The parent/guardian will be responsible to pay Zakat on the wealth of the orphan, child and insane and they can pay from the wealth of these individuals.
However, the Hanafi school considers the element of worship in Zakat and therefore opines that Zakat is not binding on the orphan, child and the insane. Since these individuals are not obliged to perform worship, they are not obliged to pay Zakat. (Regarding the case of mental incapacity, if a person has intermittent sanity, they will be required to pay Zakat as per the Hanafis. Only a person with continuous mental incapacity is exempt from Zakat).
And Allah knows best