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The 1860 census has a Jasper (no initial), 17 years old, working as a laborer, not living with his family. There is a Newton J. Siler in the 1870 census, 26 years old, married with two small children. This is probably the same person. Names are often transposed in the census. This Newton moved to Decatur County, IN and is in the 1880 census, age 36. At 75, widowed Newton J. is in Randolph County, NC in 1920, living by himself.
This doesn't give parents but it may lead to something that will.