The Shulhan Aruch (Orah Haim 616:2) rules that children under the age of 9 should not fast at all on Yom Kippur. Below age 9, according to Maran, there is no concept of Hinuch (training in Misvot) with regard to fasting on Yom Kippur, and thus these children should be fed on Yom Kippur just as they are on any other day of the year. Once a child reaches age 9, the Shulhan Aruch then writes, he or she should be trained to fast for a brief period of time. For example, if a child normally eats breakfast at 8am, on Yom Kippur he should be fed around an hour later, at 9am, so he begins training to fast on Yom Kippur. If the child is weak and it is important for him or her to eat at the regular time, the Shulhan Aruch adds, then the training should begin a year later, when the child is ready.
The Shulhan Aruch then rules that once a boy or girl reaches the age of 11, he or she is required Mi’de’rabbanan (on the level of Rabbinic enactment) to observe the Yom Kippur fast and fast the entire day. (Ashkenazim follow a more lenient view, and maintain that youngsters should begin observing the full fast later.)
However, Hacham Ovadia Yosef, in his Hazon Ovadia – Laws of Yom Kippur (p .340; listen to audio recording for precise citation), writes that Maran’s ruling does not apply nowadays, because of the weak condition of our generation in relation to past generations. Children today are not as physically capable of fasting as the children in earlier generations, and they therefore should not complete the fast until the age of Bar Misva or Bat Misva. Hacham Ovadia rules that boys at age 12 and girls at age 11 should fast until midday (as defined by Halacha), or approximately 1pm, but then the parents should force them to eat. Unfortunately, there have been incidents of children who insisted on fasting the entire day, or who told their parents they ate when in reality they did not, and ended up becoming ill, Heaven forbid. Parents should therefore see to it that their children are fed on Yom Kippur, and, as mentioned, even 12-year-old boys and 11-year-old girls should eat at midday. Hacham Ovadia applies to this issue the adage, "Al Tehi Sadik Harbeh" – "Do not be exceedingly pious." There is no value in endangering children’s health for the sake of training them to fast.
Even once a child reaches the age of Misva obligation (13 years for a boy, 12 for a girl), the parents must ensure that the child is strong enough to observe the fast. Hacham Ovadia writes that if there is even the slightest question concerning a child’s ability to fast without endangering his or her health, a physician should be consulted.
Should children be trained not to wear leather shoes on Yom Kippur, or are they allowed to wear leather shoes?
According to the strict Halacha, children are permitted to wear leather shoes on Yom Kippur, however, given the availability of comfortable non-leather shoes nowadays, children should be trained to wear specifically non-leather shoes, already from a young age.
With regard to bathing, Halacha permits washing infants and applying oil to their skin on Yom Kippur, but it is customary to be stringent in this regard. Certainly, if a child is dirty, he may and should be washed, and if an infant has a particular need to be bathed or to have oil applied, this is permissible. Under ordinary circumstances, however, children should not be bathed or have oil applied on Yom Kippur.
Summary: Children below the age of 9 should not fast at all on Yom Kippur. Children from age 9 should be fed an hour or so later than usual in the morning, assuming they are healthy and strong. At the age of a 12 for a boy or 11 for a girl, the child should fast until midday and must then be fed. Children should be trained to wear non-leather shoes on Yom Kippur already at a young age, and should also not be bathed, unless this is necessary due to dirt or because of health considerations.