At what age should kids be ordered to fast? What is the evidence on which the relevant ruling is based?

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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Children must be commanded to observe all types of worship, acts of obedience, and good morals once they become capable of understanding and discerning things. It is said that a child grows up according to what they were taught by their parents .

The age of seven is the age at which a child should start observing acts of worship. ‘Abdullah ibn ‘Amr and his father, quoted the Prophet, sallallaahu ‘alayhi wa sallam, as saying: “Command your children to pray when they are seven years old, punish them if they refuse to pray after reaching the age of ten, and put them in separate beds.” [Ahmad and Abu Daawood] 

The companions of the Prophet, sallallaahu ‘alayhi wa sallam, used to train their kids to fast at a young age. Ar-Rubayyi' Bint Mu‘awwith Al-Ansaariyyah narrated: “We (the companions) used to fast the tenth day of Muharram (‘Aashooraa’) and have our young children fast it as well. We would make them toys of wool and whenever a child cried out of hunger, we would give him a toy to play with until the time for breaking the fast came.” This hadith of Ar-Rubayyi’ is the evidence upon which the ruling that is adopted by the majority of scholars has been founded.

Allah Knows best.