All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we would like point out that if a child reaches the age of puberty [please refer to Fatwa 83431] and he has sound discretion, then he should not be denied access to his property.
Allaah says (what means): {And test the orphans [in their abilities] until they reach marriageable age. Then if you perceive in them sound judgment, release their property to them...} [Quran 4:6]
If he makes a vow, he must fulfill it, and if he breaks his oath, he is obliged to atone for it by feeding ten poor persons or clothing them. He does not have the option of fasting while able to clothe or feed ten poor persons, as we clarified in Fatwa 82135.
Feeling ashamed before his father should not prevent him from doing what is right. If he cannot withdraw money from his account, then he has to ask his father to withdraw money from his account for him in order for him to atone for the broken oath.
However, if the money is prevented from him due to his own foolishness, then the majority of the scholars are of the view that he should instead fast because he is unable to clothe and feed. The Maaliki School is of the view that it is an obligation to feed and clothe.
The Kuwaiti Fiqh Encyclopedia reads: “It is a condition for the obligation of feeding [the poor] that the person responsible is not foolish, because the money of a foolish person is withheld from him and he cannot dispose of it, even if he does something which requires feeding in atonement, such as breaking an oath, or Thihaar, or violating Ihraam. The Hanafi, Shaafi'i and Hanbali Schools are of the view that his atonement is fasting and not feeding as he is prevented from his money. However, the Hanafi School is of the view that he [a fool] must offer a sacrifice for the prohibitions of Ihraam for which fasting is not sufficient; however, he is not given the possibility of expiating immediately but rather must wait until he becomes right-minded and knows how to spend his money the right way, as he is like a poor person who does not have money. According to the Maaliki School, it is incumbent that he (a fool) gives food as an obligatory expiation from his own money, and his guardian should decide what is more suitable with regard to his money." [End of quote]
Allaah Knows best.