Here the printer’s manuscript reads “among this people”, whereas the 1830 edition reads “among the people”. The 1908 RLDS edition adopted the reading in 𝓟. A similar instance of this versus the occurs nearby in verse 11; there Oliver Cowdery initially wrote the in 𝓟 but later, it would appear, emended it to this, while the 1830 compositor set the. As argued under 3 Nephi 5:11, “I do make the record” will be accepted as the original reading.
As already noted under Helaman 14:20, there has been a strong tendency in the transmission of the text to mix up this and the, with the majority of instances involving the replacement of this with the. More specifically, we find the following cases where Oliver Cowdery replaced an original the with this (of which only one change was left uncorrected, marked below with an asterisk):
And we also have the nearby case in 3 Nephi 5:11 where it appears that Oliver consciously decided to change the record to this record.
On the other hand, we have two cases where the 1830 compositor set the instead of this (of course, both of these changes were permanent):
The first of these appears to be due to editing on the part of the 1830 compositor (see the discussion under 2 Nephi 10:23). So when we compare the number of permanent changes (including cases that could have involved editing), we find that there are two instances where Oliver Cowdery replaced the with this and two where the 1830 compositor changed this to the. Thus there is no strong evidence from errors in transmission that favors either this or the here in 3 Nephi 5:12.
Neither reading (“among this people” or “among the people”) is completely satisfactory. It should be noted that Mormon’s specific statement about the church being established “among them after their transgression” apparently refers to the original people of Alma, who had broken away from the people of Noah (as described in Mosiah 18). The transgression mentioned refers either to the general apostasy of the people under king Noah or, more specifically, to the execution of Abinadi, a prophet of God, by the king and his people (king Limhi’s characterization in Mosiah 7:24–26). The use of this seems to be what Mormon intended, but then realizing that his use of this might be confusing, he added the yea-clause to explain what he meant by “the church among this people” (namely, “the first church which was established among them after their transgression”). One could further argue that the reference here in 3 Nephi 5:12 to Alma establishing the church “among this people” is based on the language in Mosiah 26:17: “and blessed art thou because thou hast established a church among this people” (here the Lord is speaking to Alma). Based on internal evidence, the slightly more probable reading for the original manuscript in Nephi 5:12 is “among this people”.
Summary: Restore the reading of the printer’s manuscript in 3 Nephi 5:12 (“among this people”) since the use of this is more specific and helps to explain why Mormon wrote the following yea-clause, “yea the first church which was established among them after their transgression”.