My recent lecture on researching the poor focused on Georgia records, but truthfully, many of the records I used as examples can also be found in other states, albeit in different forms. Here is one example of a court record establishing support for an illegitimate child. Note that this one record names the child and her age, both her parents, and her grandfather.
Minutes of Monday Jan. 20th 1840
State & Elizabeth Smith vs Larken Johnson } Bastardy
Ordered by Court that Larkin Johnson pay the sum
of sixty Dollars for the maintenance of Elizabeth Smiths
bastard Child of which he stands convicted as the reputed
father as appears of records and that Sci-fa issue to
him to appear at next Court & show Cause if any he
have why Exceution [sic] should not issue for the same
Barbary Smith the infant Bastard Child of Elizabeth
Smith be bound to Joseph Smith the Grandfather till she
attain the age of 18 now being two years old
Sci fa issued 16 May 1840
Source: Macon County, North Carolina, County Court Minutes Book 3, 1838 – 1855: 67; North Carolina State Archives, Raleigh; NCSA micropublication C.061 30001.