The 1840 edition has beside instead of besides. This is undoubtedly a typo and not an example of Joseph Smith’s editing for that edition. Elsewhere in the current text, there are two occurrences of besides with the meaning ‘in addition to’ (but none of beside with this meaning):
Interestingly, in the last instance, the 1906 LDS edition accidentally replaced besides with beside, but that error was not continued since that edition never served as a copytext for subsequent LDS editions.
Originally there was a beside in 1 Nephi 2:6 (“he pitched his tent in a valley beside a river of water”), but this unique instance of beside was edited by Joseph Smith to by the side of (see the discussion under that passage). Of course, this instance of beside does not mean ‘in addition to’.
Summary: The 1840 change in Alma 57:6 of besides to beside is a typo rather than the result of editing by Joseph Smith; a similar change occurred in the 1906 LDS edition for Mormon 3:21; the critical text will maintain all three original instances of besides, each of which has the meaning ‘in addition to’.