The original text here had a multiple negative, nor neither. The 1840 edition changed neither to either, most likely the result of Joseph Smith’s editing for that edition. The LDS text made the change to either in the second printing of the 1852 edition, undoubtedly as a result of consulting the 1840 edition.
There are no other instances of this usage nor neither (or nor either) in the original text. There are, however, similar examples of nor followed by an n-initial negative word, such as nor never (see under Jacob 7:9) and nor no (see under Mosiah 2:12–13). The critical text will restore all instances of multiple negation whenever they are supported by the earliest textual sources. For a general discussion of multiple negatives in the original text, see under negation in volume 3.
Summary: Restore in Alma 23:1 the original multiple negative nor neither (“that they should not lay their hands on Ammon or Aaron or Omner or Himni nor neither of their brethren”).