Is it permissible to give charity or pay Zakat with the intention of settling the debt of a deceased father, if the creditors are unknown?

May Allah reward you for your effort in searching for your father's debts to repay them. This is an act of filial piety towards him after his death. The default is that his financial liability is clear unless a debt is proven against him. There is no harm in giving charity on his behalf with money, and your intention should be for the reward to reach him, not to pay off an unproven debt, because the default is that his liability is clear. Assuming there was a debt owed by him, charity does not absolve him of it; rather, rights must be delivered to their owners, and if delivery is impossible, then charity is given on their behalf.