The Child is not obligated to fast, but he may be ordered to do so
Question :
My small child persistently fasts Ramadhan even though fasting is harmful for him due to his young age and his sickly health. Should I use harshness with him to force him to break his fast?
Answer:
If he is a child who has not reached the age of puberty, then he is not obligated to fast. However, if he is able to fast without difficulty, then he should be commanded to do so. The Companions used to make their children fast. This was to such an extent that if a child among them cried they would give him some toys to distract him (from thinking about food). However, if it has been confirmed that this harms the child, then he should be prevented from it. If Allâh, the Most High has prevented us from giving the children their wealth due to fear of corrupting it, then verily fear of harming the bodies is even more important for them to be prevented from. However, preventing them should be in a way that is not harsh, for verily harshness should not be used in dealing with children when raising them.
Source:
Ash-Shaykh Ibn 'Uthaimin
Fatawa Islamiyah, Vol. 3 Page 328