What is the ruling on the jewelry that the aunt gave to the mother for adornment, then the aunt passed away, with the mother being unaware of the original owner of the jewelry?

If the gold belongs to your mother's maternal aunt, then your mother must pay it to the aunt's heirs for them to divide it according to Islamic law, because the basic principle is that what a Muslim possesses is his property. If someone claims the gold belongs to him, he must provide legal proof, which is a man and two women, or a man and the claimant's oath.