The Confederate stuff is him. Not sure about the NY tax document being him. I know he he was here after the war up until his death in the 1880s. I've run across the NY/NJ Hosea before on Ancestry. I may doing some checking to make sure. On the Census each time he listed he was born in SC. I believe he was in Greenville County, SC in 1850 but the name was spelled "Hezeh" on that Census. I know they pronounced it "Hosey" and sometimes it is spelled that way on some documents.
Thanks for looking.
Dear Mr. Hammond,
Thank you for posting your request on History Hub!
We have searched out catalog and have located Carded Records Showing Military Service of Soldiers Who Fought in Confederate Organizations , 1903 - 1927 of the War Department Collection of Confederate Records (Record Group 109) that includes two files Confederate Soldiers from the State of South Carolina - Hammond, Hosea - Twenty-second Infantry F-H and Confederate Soldiers from the State of South Carolina - Hammond, Hosea - First Battalion, Sharp Shooters. The records are digitized and are available via the Catalog.
We also located the Population Schedules for the 1840 Census in the Records of the Bureau of the Census (Record Group 29) that may include the Hammond family. Please note that the 1840 census and earlier census only listed the Head of Household and then the ages & gender of the various members of the household. For access to these non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
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You may wish to search Ancestry or FamilySearch for the U.S. Census. There may be a fee for using Ancestry. Instead, please check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
Please refer to NARA’s website about Census Records and the FamilySearch Research wiki Beginning Research in United States Census Records for information on how to search the Federal Census Schedules.
We hope this is helpful. Best of luck with your family research!