Can you tell us a bit more about the history of the school?
What was the actual geographical location?
In what census Year schedule do you find your Anthonys who attended the school?
Could the name of school have a variation?

Reading the section on Harrison County in The Handbook of Texas and its demographics gives clues of where to search to try and find the information you are seeking.

Your best bet may be to dash a letter of inquiry to the Secretary of State. Any school operation would need to have applied for a license to operate. This application is likely to still be on file.

Second a letter to the State Board of Education may reveal a historical survey/report of all such schools in operation for whatever period.

Third a letter to the local historical or genealogical society may bear fruit.

Fourth a review of local legal proceedings [ and newspapers] may detail the opening as well as the closing of such school.

Is it likely that the physical operation was a church? What churches were in the area where the Anthonus lived? Are any of those in operation today?

A query in the bulletin of all of the current churches as well as schools in the area may turn up a gold mine of information.

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A query to the TX-AfriGeneas@yahoogroups.com mailing list may be helpful.

Other suggestions for Gwen everybody?