Only sane adults have to give Zakaat
In the opinion of the Hanafi jurists, Zakaat isn’t Compulsory (Wajib) in the wealth of a minor. As Zakaat is a monetary form of worship and the Shariah isn’t applicable to a minor. In the same way, Zakaat isn’t compulsory on lunatics as well. The Holy Prophet (Sallallahu alaihi wa sallam) has declared minors and lunatics to be exempted:
Translation: It is narrated on the authority of Hadhrat ‘Ali (May Allah be well pleased with him), he relates from the Holy Prophet (Sallallahu alaihi wa sallam): The Holy Prophet (Sallallahu alaihi wa sallam) said: The pen has been lifted from 3 people (i.e. they are exempted): A sleeping person until he awakes, from a child until he becomes a major and from a lunatic until he becomes sane. (Sunan Abu Dawood, Hadith No. 4405)
As ‘Allama Ibn Nujaim Misri (May Allah shower His mercy on him) has written in Al Bahr Ur Raaiq Sharh Kanz Ud Daqaaiq, Vol. 2, Pg. No. 354.