This designation you have is for a pension application for service in the War with Mexico.
Josiah KELLET, Soldier's Application SA-23011, dated 5 Aug 1890, filed in Missouri; Widow's Application WA10460, for service in Phillips' Co.(no other service noted)
There is also a separate entry as follows:
Josiah KELLETT, widow Mary Jane; widow's application WA10460, dated 5 March 1892, filed in Arkansas; and soldier's application filed in Missouri SA-23011, for his service in Phillips' Co. Arkansas Volunteers.
There is also another entry which might be a brother to your Josiah Kellett:
Austin Kellett, soldier's certificate SC16880, dated 31 July 1888, filed in Arkansas for his service in Co. D, Calhoun's Battalion, Georgia Mounted Volunteers; and Old War record I-25607.
Perhaps if you write to the NARA and give them both application numbers for Josiah, as well as the application number for his widow, they can then find the file.