Is it permissible to use a father's bank account, deposited in a usurious bank, to participate in a religious competition, such that monetary prizes would be sent to it?

The general rule for opening an account in a usurious bank is that it is forbidden, due to its involvement in aiding sin. An exception to this is made in cases of necessity, such as protecting money from loss or for transferring a salary if the employer mandates it, provided there is no permissible alternative, like an Islamic bank.

Based on this, it is permissible to use the father's account for the aforementioned purpose (registering for a competition) if no Islamic bank is available, and the bank does not benefit from the mere registration of the account.

If you win a financial prize, you must withdraw it quickly unless there is a fear of its loss, because necessity is determined by its extent.