Zachariah Landrum's 1803 claim was on Laura's Creek west of the Tombigbee River below the old Choctaw line in Washington County, Mississippi Territory, not Alabama. Alabama Territory was cut from the Mississippi Territory in 1817 and Alabama became a state in 1819.
In 1803, Washington county Mississippi Territory was quite large and encompassed most of present day southern Mississippi and southern Alabama. I am not sure where Laura's Creek was located. The Old Choctaw Line was a north/south boundary between the Choctaw lands on the north and the Creek lands on the south. This line follows along the border between modern day Clarke and Marengo Counties, Alabama.
So all we know is that Landrum's land was west of the Tombigbee River and south of the Choctaw line which would be somewhere in present day southern Choctaw or Washington County, Alabama.
Zachariah Landrum registered land in 1811 in "Washington County, Mississippi Territory" and when Alabama Territory was formed in 1817, this area became both Washington and Clarke Counties of Alabama. By 1819 he lived east of the Tombigbee River in present day Marengo County, Alabama.
I hope this helps.