Is it obligatory to pay a debt claimed by someone from a deceased person without proof, and is requesting him to swear by Allah contrary to Sharia?

There is no obligation to pay anything to someone who claims a debt against your father without knowledge or evidence, even if the claimant swears an oath. This is because the oath is not directed to him; rather, he is required to provide evidence. The Prophet, peace and blessings be upon him, said: "Were people to be given according to their claims, some people would claim the blood and wealth of others. But the oath is upon the defendant," and "The burden of proof is on the claimant, and the oath is on the one who denies." His mere oath is not valid Shariah evidence. If he insists, then the matter should be referred to a Shariah court.