Back in On Monday, May 4th, 2020, The F.D.A. had announced that companies who are selling CONVID-19 coronavirus antibody tests must submit data to the F.D.A. The link directly below is an updated F.D.A. site that lists the companies and their data that had been provided performance data for their Serology Test.  These are the test to use; one should crosscheck your medical providers test against the listed test if you are planning on having an Antibody test done.

F.D.A. - E.U.A. Authorized Serology Test Performance  (29 test at last count)

An important fact to keep in mind is, even though one has the Antibody, it is not yet known if that provides immunity from Coronavirus. Conclusions about protection have yet to have been verified. Note:  Companies with new test must submit their data and an application within ten days of their plans to marketing their product.

Below are two older links to significant news site articles with some more details.

Washington Post F.D.A. steps up scrutiny of coronavirus antibody tests to ensure accuracy

New York Times - F.D.A. Orders Companies to Submit Antibody Test Data