Answered by Shaykh Abu Usamah
Is zakat due upon a child that hasn’t reached the age of puberty? If the money was saved for the child from gifts, and the money was kept in the bank for a number of years, will the zakat payment be the responsibility of the parents- to deduct the applicable amounts. If the zakat wasn’t deducted, will this amount be due at the point the child reaches puberty from all previous years?

Al-Salam `alaykum
One of the conditions for Zakah becoming obligatory on a person is maturity (bulugh).
Thus a child, who has not reached the age of puberty, is not liable for Zakah on any assets he or she possesses. It is therefore not required to deduct any amount for Zakah for previous years. Upon reaching puberty the Zakah year of such a child, who possesses Zakatable assets, will begin and the first payment of Zakah will be made one year after this date.
(Al-Durr al-Mukhtar with Hashiya ibn Abidin 2.280, Dar al-Fikr 1995)