In South Africa, a child of a foreigner has two options (dependant on their age and what category the foreign parent's temporary residence permits hold)

The first would be a study permit - a foreigner who would like to study in an educational institution would require a South African study permit (temporary residency). 

Foreign families immigrating to South African with children from the age 6 to 16 (as all children from the age of 6 to 16 are required by law to attend schooling, therefore, requiring a South African study permit).  If a child is young enough to attend crèche, pre-school, etc, provision may be made by the Department to issue a study permit to the child(ren), this is done with their own discretion.  These permits are issued to the length of the schooling period, the maximum period length of a study permit is 3 years and these permits can be extended a number of times.