Here is a list by county of members of the Peters family who were free by 1813. Many of them are from the Peters family on my site.
Paul

James City County

"Free Persons of Colour above 16 years."
Some have “freed by”and their former master’s name.
Others have “Cold man” or “mulato” after their name.

Thomas Peters 1, 2 total (apparently his wife)

Mathews County

A List of Free Negroes & Mulattoes over 16 years.

Robert Peters free negro 1

Middlesex County

List of Free negroes subject to Taxation

Betsey Peters
Lucy Peters

Northumberland County
Molley Peters 0 males, 2 females
John Peters 1 male
Joseph Peters 1 male

York County
Anthony Peters 1, 2 total

Surry County
Betsy Peters
Jesse Peters

Henrico County
List of Blacks above the age of 16
Jim Peters
Tom Peters

City of Fredericksburg
Free Negroes & Mulattoes
Lucey Peters (M)

City of Richmond (1814)
James Peters
John Peters
David Peters