David was born in 1801. He passed away in 1862.
1830; Census Place: Hyde, North Carolina; Series: M19; Roll: 121; Page: 278; Family History Library Film: 0018087.
North Carolina, Death Certificates, 1909-1976, North Carolina State Archives; Raleigh, North Carolina; North Carolina Death Certificates, Ancestry.com, North Carolina, Death Certificates, 1909-1976 (Provo, UT, USA, Ancestry.com Operations Inc, 2007), Ancestry.com, North Carolina State Archives; Raleigh, North Carolina; North Carolina Death Certificates.
Ancestry.com, Virginia, Select Marriages, 1785-1940 (Provo, UT, USA, Ancestry.com Operations, Inc, 2014), Ancestry.com.
Ancestry.com, U.S., Find A Grave Index, 1600s-Current (Provo, UT, USA, Ancestry.com Operations, Inc., 2012), Ancestry.com:
Name: David Carter Jr Gender: Male Birth Date: 26 Jan 1801 Birth Place: Mount Pleasant, Hyde County, North Carolina, United States of America Death Date: 23 Jun 1862 Death Place: Mount Pleasant, Hyde County, North Carolina, United States of America Cemetery: Fairfield Cemetery Burial or Cremation Place: Fairfield, Hyde County, North Carolina, United States of America Has Bio?: N Father: David Carter Spouse: Sarah Lindsay Carter Children: Henry Clay Carter Isaiah Spencer Carter Frances Ann Carter James Henry Carter Frances Ann Fletcher Spencer Laura Elizabeth Blackwell Peledge Spencer Carter URL: https://www.findagrave.com/mem...
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https://www.findagrave.com/memorial/40689155/david-carter
Both of these sources indicate that this David Carter, Jr. is the son of his father's second wife, Bethiah Farrow.