It seems a little extraordinary.
It's possible that some people who think you've inherited a packet have been gossiping and some want to try to take advantage.
But maybe your father was in financial trouble, or was financially irresponsible, and left behind him a trail of secrets.
Find out the law. There is probably a statute of limits on bad debts.
If the limit has not been reached, ask them to show you documentary proof.
In some situations, proof may not be available. Then you would have to treat each case on its own merits, but do ask trick questions, to which only you know the answer, to try to get a sense of the truth.