Prince -- Woman Warns Estate ... Step Aside, I'm His Wife!

Prince was married when he died and wanted all of his money to go exclusively to his wife -- according to the alleged wife, who's now putting his estate on notice.

The woman -- Claire Elisabeth Elliott -- filed a request for the court to remove Bremer Trust bank as administrator of Prince's estate, because she believes she should be calling the shots ... as his "Sole Heir."

Claire even claims there is a marriage certificate and will to back her up. It's worth noting she did not attach those documents in her filing. Also, we checked Minnesota court records ... no dice.

We're gonna go ahead and file this under "can't knock her for trying." She is ambitious though -- Claire also filed docs to run for President ... of the United States.

Just a hunch, her shot at Prince's dough will likely end the same way as her campaign.