A Child's Good Deeds: For Whom are they Written

Question :

Are the good deeds performed by a child (i.e. who has not reached puberty) written for him or for his parents, deeds such as prayer, Hajj, recitation of Qur'an? And may Allah's peace, mercy, and blessing be upon you.

Answer:

When a child who has not reached puberty performs good deeds, the rewards of those deeds are his, belonging neither to his parents nor to anyone else. However, a parent does get reward for teaching a child to do good and to helping him in performing good deeds. During the Farewell Pilgrimage, a woman lifted up a child, and while pointing to it, said, "O Messenger of Allah, is there a Hajj for this one?" He said:
"Yes, and for you is reward."

The Messenger of Allah ﷺ informed us that the child's Hajj is his and that the mother is rewarded for taking him on the pilgrimage. This principle of receiving reward for helping others does not apply only to parents, but also to others who teach orphans, relatives, and servants, for the Messenger of Allah ﷺ said:
"Whoever guides to goodness receives a reward equal to the person who does it (i.e. a good deed)."

Allâh Almighty rewards his servants for working together in promoting righteousness and good deeds.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 8 Pages 397-398