All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
The mentally handicapped isn`t held accountable for not performing obligatory prayers and fasts and not paying fast ransom as well. This is attested to by the following narration where the Prophet (PBUH) said (What means):" There are three (persons) whose actions are not recorded: a sleeper till he awakes, a boy till he reaches puberty, and a lunatic till he comes to reason.” [Abu Dawood]. "
The insane and the infant aren`t held accountable for not performing acts of devotion since their actions aren’t recorded.”{ Moghni Al-Muhtaj, Vo.2, P.170}. However, the guardian is obliged to pay Zakat-ul-fitr on behalf of the insane person mentioned above since he (guardian) is accountable as well to pay it on behalf of his dependants (wife & children), even if they aren`t accountable yet for adhering to the commands of Sharia.
This is because Ibn ’Umar (may Allah be pleased with him) narrated, The Messenger of Allah (PBUH) enjoined the payment of one sa` of dates or one sa' of barley as Zakat-ul-fitr on every Muslim, slave or free, male or female, young or old, [Al-Bukhary]. And Allah the Almighty knows best.