During the Civil War Moses enlisted in the 74th U.S.C. Infantry as part of the 2nd Louisiana Native Guard Infantry. 
In 1870, he is living with his wife Margarette (age 23), daughter Louisa (age 2), and son Robert (age 8 months) in New Orleans. 
In 1880, he and his family are living with his mother and stepfather Charlotte & Robert Noles. His family includes his wife second wife(?) Margaret (age 22), son Robert (age 11), and son John (age 8). 
In 1900, he and his family are listed as living on Lee's Lane in New Orleans, the census data indicates that he and Margaret have been married for twenty years and that she is the mother of four children with two living. A grandson Moses (age 10) is living in the same household.
In 1910, he is listed as Rev. Mose Anderson, with occupation listed as Preacher, the census data indicates he and Margaret have been married thirty years, again she is listed as the mother of four children with two living. His son John (age 42) and his family are living in the same household.
↑ "United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MS5R-2YG : accessed 22 February 2018), Moses Anderson, 7th Precinct New Orleans city Ward 15, Orleans, Louisiana, United States; citing enumeration district (ED) 141, sheet 10B, family 209, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,576.
↑ The National Archives at Washington, D.C.; Washington, D.C.; NAI Title: General Index to Civil War and Later Pension Files, ca. 1949 - ca. 1949; NAI Number: 563268; Record Group Title: Records of the Department of Veterans Affairs, 1773 - 2007; Record Group Number: 15; Series Title: U.S., Civil War Pension Index: General Index to Pension Files, 1861-1934; Series Number: T288; Roll: 9
↑ "United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MDXH-V5P : 15 August 2017), Moses Anderson in household of Robert Noles, New Orleans, Orleans, Louisiana, United States; citing enumeration district ED 89, sheet 450C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0464; FHL microfilm 1,254,464.
↑ "United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MPYG-BW3 : accessed 22 February 2018), Reverend Mose Anderson, New Orleans Ward 15, Orleans, Louisiana, United States; citing enumeration district (ED) ED 239, sheet 5A, family 136, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 525; FHL microfilm 1,374,538.
↑ Ancestry.com. Louisiana, Statewide Death Index, 1819-1964 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2002. Original data: State of Louisiana, Secretary of State, Division of Archives, Records Management, and History. Vital Records Indices. Baton Rouge, LA, USA.
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It may be possible to confirm family relationships with Moses by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Moses: