I've done the Y-DNA test with familytreedna.com and know who Joseph's distant ancestors were, but I've been unable to follow the historical record trail to connect the dots to his father and to the grandfathers that stretch between him and our first US emmigrant ancestor Thomas Cox, vintner, born 1641 in England.
My Joseph Cox first appears in the historical records on the 1850 US Census for Joshua Township, Fulton County, IL. He is listed as a 14 year old in the household of Henry S. Marvial [sic. Marvel]. I've been unable to connect him genetically to the Marvel family or to their spouses' families or to any Cox family listed on the 1850 Census. I've found no probate or land deed records in Fulton or surrounding IL counties that imply a connection to Joseph. The only result of my years of searching is an arguable link to a John Cox found on the 1840 US Census for that township. The argument rests weakly on two facts. The John Cox listing enumerates three males under the age of 5, born about 1836, Joseph could have been one of them. Also, many of the household names that closely bracket the 1840 John Cox listing can be found on the 1850 US Census closely bracketing the Marvel listing.
My study of the Marvel family indicates they arrived in the area circa 1845, living for a while at Rapatee, Knox Couny, IL before moving to Joshua, Fulton County, IL.
There was an additional Cox/Marvel connection found by Cathy Parsons, a Fulton County, IL genealogist. According to a Fulton County Marvel family history, a younger brother of the Henry Marvel mentioned above, Marmaduke Marvel, his wife, and newly born daughter in 1857 "with the brother Francis Marvel and a friend, Nathan Cox, started for the state of Texas." In 1859, Marmaduke and family returned to Fulton County from Alvarado, Johnson County, TX. The 1860 US Census for Alvarado, Johnson County, TX lists a Nathan Cox, age 27, born in IL, a farm laborer living with the Richard Graves household. There are no other Cox listings for that county.