All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your father had died after the Zakaah had become obligatory on his wealth, then you are obliged to pay the Zakaah of his wealth and distribute it among the people who are eligible for it as he was obliged to pay it before he died. The Zakaah should be paid before distributing the inheritance among his heirs as it is like a debt which he is obliged to repay as the Zakaah had become other people’s right after it had become due.
In case he had died before the time when he pays the Zakaah on his money comes, then Zakaah is must not be paid on it and you are not obliged to pay it as it had not already become due until one lunar year elapses on it. This is the view of the scholars on this issue.
Allah knows best.