What should I do with the money of my deceased apostate father, and should I pay off his debts, knowing that a Muslim does not inherit from a non-Muslim and that my paternal uncles and aunts claim that the money originally belongs to them?

A warning regarding the grave danger of declaring a specific individual an apostate. If your father died as an apostate, the jurists have differed concerning the fate of his wealth: 1. The wealth becomes fay' (spoils) for the public treasury (the opinion of Malik, Al-Shafi'i, and Ahmad). 2. The wealth goes to his Muslim heirs (the opinion of Abu Yusuf and Muhammad). 3. What he acquired during his time in Islam goes to his heirs, and what he acquired during his apostasy goes to the public treasury (the opinion of Abu Hanifa).

The first opinion is the one usually issued as a fatwa. However, if the state does not fulfill its duty towards the public treasury, there is no harm for the heirs to adopt the second opinion, because his Muslim relatives are more deserving of the wealth.

As for debts and financial claims, it is necessary to establish شرعية (legitimate) evidence for them, unless the mature and sound adult heirs corroborate them. This is based on the saying of the Prophet, peace be upon him: "If people were given whatever they claimed, then some people would claim the blood and wealth of others. But the oath is upon the defendant." Evidence can be established by one man and two women, or one man and the claimant's oath. Whoever establishes evidence is given their right, and whoever does not establish it receives nothing.