"The Battle of Baton Rouge O.R. reports has a Union officer protesting to Confederate authorities of the use of a "Black corps" during the battle of August, 1862."

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It' possible. And there was more than one company of black troops in that area (Baton Rouge, Pointe Coupee, St. John Baptist, &c).

But a lot more evidence is needed. Something like- "Dear Sis, I seat myself to write you a few lines.......a company of colored soldiers fought with us at Baton Rouge...."