The singer died in April from an accidental overdose of the painkiller fentanyl, but he did not leave a will and did not have any children.
Reports in Minnesota say his estate may be worth at least $300m (£227m).
A judge has now ordered genetic tests to be carried out on six people with claims to be relatives of the singer.
Four siblings or half-siblings, as well as two women believed to be a niece and a grand-niece, will be tested.
Genetic tests had already ruled out the claim of a man in jail in Colorado who said he was Prince's son.