This doesn't mean that Mary Ann Cox filed a claim at Little Rock on January 2, 1863. It means that, according to her claim, her husband died at Little Rock on January 2, 1863.

When the 33rd Arkansas sent out feelers for the status of its absent men, in order to fill out the April 30, 1863, muster roll, they were told that Samuel F. Cox died aboard a boat on or about December 28, 1862. In fact, this is just about when the boat would have reached Little Rock from Van Buren. Record keeping (especially in the Trans-Mississippi Department) being what it was, the initial report may have stated that he was discharged from the hospital boat on that date, and was misconstrued by the regimental orderly that he had died on that date. Mary Ann Cox's affidavit, on the other hand, was based on a sworn statement that Samuel F. Cox had died in a hospital on January 2, 1863.

At the time that the list of families of indigent soldiers was compiled, Mary Ann Cox had probably been informed that her husband was "thought dead." This information likely came from a member of the regiment, either by letter or directly from a soldier on furlough. At some point subsequent to this, she apparently received a notification as to his official status, including date and place of death. This enabled her to file a claim for his accrued pay and allowances.

Is the James Cox you're looking for the man who was living in Mine Creek Township of Hempstead County, born c1832 in Georgia? If so, I can help you there. Just let me know.