We have all heard of sons saying the Kaddish.
What about small children? Surprisingly, even small children do say the Kaddish, and it is one if the most pitiful and moving experiences to hear a small child say Kaddish after their father or mother.
Although children are not qualified to lead the service, they may, and are encouraged to, say the mourner's prayer.
Obviously, very small children are not capable of saying the Kaddish in a proper way, and are not encouraged to say it at all.
They will say it when they grow older, on their parent's Yortzeit, or anniversary of death.
What about someone mentally defective, like some autistic or retarded.
Do they say Kaddish too? As a rule, if they can manage the job, they do go ahead and say it.
They, as a minor, do not help form the quorum nor lead the congregation, but they do count for kaddish.
In fact, in view of this, we designate a special Kaddish for them, one after the service, called "the orphan's Kaddish".
This is the Kaddish said after the "Ulainu" prayer.
It is customary that when a small child or someone mentally defective says the Kaddish, an adult stands near them to ease them over any rough spots until they get the hang of it and can say the Kaddish with confidence on their own.
Great sages in Israel have been known to take time off to teach young orphans the Kaddish and coach them on it until they felt ready to do it alone.
What about women? Common Jewish custom is that daughters, big or small, do not recite the Kaddish, although there is extensive literature in the Halachik responsa discussing indeed why not, and when even they ought to say the Kaddish.