Paying zakaah from a child’s wealth for past years

Firstly:

Whoever has failed to pay zakaah for past years has to pay
it, whether he omitted to do so knowingly or out of ignorance. Shaykh Ibn
Baaz (may Allaah have mercy on him) was asked about someone who did not pay
zakaah for five years out of ignorance. He replied: 

You have to pay zakaah
for all the past years. Your being ignorant does not mean that it is waived
for you, because the obligation of zakaah is a well known part of the
religion which no Muslim has any excuse for not knowing, and the ruling is
not concealed from the Muslims. Zakaah is the third pillar of Islam. So you
must hasten to pay zakaah for all the past years, as well as repent to
Allaah for delaying it. May Allaah forgive us, you and all the Muslims. And
Allaah is the Source of strength. 

End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz,
14/239 

See also question no.
21715 

An exception from that is zakaah on kinds of wealth where
there is some scholarly dispute as to whether zakaah is due on them, such as
jewellery that is used. Whoever does not pay zakaah on it out of ignorance,
or because he follows a Shaykh who says that zakaah is not due on it, then
he does not have to pay zakaah on it for the past, but he should pay zakaah
on it once he knows that it is subject to zakaah. 

This was also stated in a fatwa by Shaykh Ibn Baaz (may
Allaah have mercy on him) who said: We also draw attention to the fact that
it is obligatory to pay zakaah once you know that it is required on
jewellery, but with regard to the past years before knowing that it was
required, you do not have to pay zakaah for that, because the rulings of
sharee’ah only become binding after one learns of them, and because there is
a scholarly difference of opinion on this issue. End quote from Fataawa
Islamiyyah, 2/84 

Secondly: 

The majority of scholars are of the view that zakaah is due
on the wealth of minors, and that being a minor does not mean that the
obligation to pay zakaah is waived. 

Ibn Qudaamah (may Allaah have mercy on him) said: Zakaah must
be paid on the wealth of minors and the insane. That was narrated from
‘Umar, ‘Ali, Ibn ‘Umar, ‘Aa’ishah, al-Hasan ibn ‘Ali and Jaabir (may Allaah
be pleased with them all). It was also the view of Maalik, al-Shaafa’i and
Ahmad. End quote from al-Mughni, 2/256. 

This has already been discussed in the answer to question no
75307. 

Thirdly: 

Not all shares are subject to zakaah. Some of them are
subject to zakaah and in other cases, zakaah is only due on the profits, if
they reach the nisaab and one year has passed. For more information on that,
please see the answer to question no
69912 . 

If these shares are subject to zakaah, then he must pay
zakaah for the past years.  

If zakaah is due on their profits only, then he must pay
zakaah on the profits that reach the nisaab, after one year has passed. 

And Allaah knows best.