Is Zakat obligatory on the children's money saved in separate accounts for each of them when the Zakat threshold is reached for each account individually, or when their total reaches the Shar'i threshold?

If a boy possesses wealth through legitimate ownership, and this wealth reaches the nisab (definition) (minimum taxable amount), zakat (definition) becomes obligatory on it upon the completion of a full year from the day it reached the nisab. This is based on the general import of Allah’s statement: "Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase," (Quran 9:103) and the Prophet’s (peace be upon him) saying: “Inform them that Allah has enjoined upon them a charity on their wealth, to be taken from their rich and given to their poor.” If the share of each of the four children reaches the nisab, then zakat for his wealth is to be paid, and this has no bearing on the wealth of the other siblings.