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I did not find the 1870 census, but I did find one for 1860. If you click on the name C. Baer at top of page it will take you to email. perhaps you can contact he/she about the 1870.
I will keep looking and let you know if I find anything else.
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Dear Mr. Martinez,
Thank you for posting your request on History Hub!
Since the Wampanoag Tribe of Gay Head (Aquinnah) did not receive Federal acknowledgement as an Indian Tribe until 1987, they were not separately censused in 1870. We searched the National Archives Catalog and located the Population Schedules for the 1870 Census, in the Records of the Bureau of the Census (Record Group 29) that would include individuals from the Gay Head locale. Native Americans were noted with an “I” or “In” within the 1870 census. For access to and/or copies of these records, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
You may wish to search Ancestry.com for the 1870 U.S. Census. There may be a fee for using Ancestry. Instead, some of the images from Ancestry are available for free on Family Search or at your local library. Many library systems subscribe to these sites, making them free for patrons.
We hope this is helpful. Best of luck with your research!
[Some information provided by Cody White, Subject Matter Expert]