Miriam Anderson's parents are most probably Cornelius Anderson and Anna Redmon. Some researchers have insisted her surname was Williams, but there seems to be no evidence to support that conclusion.
This confusion may be because Miriam is a half-sister of Elijah Anderson's first wife, Frances Williams. Miriam and Frances have the same mother, Anna Redmon, whose first husband was Robert Williams.
Some useful information on this can be found at "Descendants of Bartholomew Anderson" at this site: http://homepages.rootsweb.ancestry.com/~anderson/va/trees/barth.html. There Miriam Anderson is a daughter, the second child, born to Cornelius Anderson and Anna Redmon and it states that "Miriam Anderson m. Elijah Anderson (as his second wife)", so there is no doubt this is the same person.
"Virginia, Marriages, 1660-1800" by Jordan Dodd and published by Ancestry.com Operations Inc, 1997, gives the date and place of her marriage to Elijah Anderson AND GIVES MIRIAM'S SURNAME AS ANDERSON.
One final bit of evidence: It is said that Cornelius Anderson died in Circleville, Pickaway, Ohio. This is where Nancy Anderson, daughter of Miriam Anderson, is living and the first 9 of her 13 children are born there. Is it conceivably just coincidence that Cornelius dies in the same far-away little town in Ohio where Nancy Anderson Shaw is living? No. It's more reasonable to think that Cornelius is Nancy's grandfather.
Miriam and Elijah were married on 6 November 1794 in Frederick County, Virginia.[1]
Miriam was born about 1762.
MemorialFind a Grave, database and images (https://www.findagrave.com/memorial/106659813/miriam-anderson: accessed 07 December 2023), memorial page for Miriam Anderson Anderson (1777–1803), Find A Grave: Memorial #106659813; Burial Details Unknown; Maintained by No Reins (contributor 46595053).
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