1920 census makes this family clear. There is a strong possibility that J N's given name was Josephus, not Joseph.
The state abbrev after the census year is the birth state.
I speculate that the 1870 record is Nancy (Clardy) Slaten and daughter Martha:
Slaton N C 1870 NC Cen Anderson (710) Williamstwn SC 1820 fem Slaton M C 1870 SC Cen Anderson (710) SC 1852 fem
I speculate that Newton and Josephus N are the same person:
Slaten Nancy 1880 SC Cen Anderson (173)D Pendleton SC 1811 widfSC mSC Slaten Martha L 1880 SC Cen Anderson (173)D SC 1852 dau m?Newton fSC mSC Slaten Newton 1880 SC Cen Anderson (173)D SC 1871 son? Martha L
PATRICK William P 1920 SC Cen Franklin 37 10A GA 1853 67 f-i-l Jos fSC mSC KELLY Marta L widowed 1920 SC Cen Franklin 37 10A GA 1853 67 moth Josephus Slaton Josephus N 1920 SC Cen Franklin 37 10A Lavonia GA 1872 48 h Alice N fSC mSC Slaton Alice N 1920 GA Cen Franklin 37 10A GA 1883 37 w Josephus fGA mGA Slaton William S 1920 GA Cen Franklin 37 10A GA 1904 16 s Josephus Slaton James H 1920 GA Cen Franklin 37 10A GA 1905 15 s Josephus Slaton Walter P 1920 GA Cen Franklin 37 10A GA 1907 13 s Josephus Slaton Wallace N 1920 GA Cen Franklin 37 10A GA 1909 11 s Josephus
I have an electronic book and some cousins to this line on my website. Please let me know if you are interested,a t: email@example.com
This posting should NOT be under this heading, so I am going to put the query and response under one posting.