Here the 1837 edition replaced “the synagogue” with “their synagogue”. Either reading (“the synagogue” or “their synagogue”) will theoretically work. Earlier in verse 5, the text established that Aaron had “entered into one of their synagogues”, so “the synagogue” is perfectly acceptable here in verse 11. In fact, “their synagogue” implies that they had only one in the city of Jerusalem, which would be incorrect:
In fact, the two instances of “their synagogues” in verses 4 and 5 may have prompted the 1837 compositor to set “their synagogue” in verse 11. The critical text will restore the original use of the before synagogue in Alma 21:11.
Summary: Restore in Alma 21:11 “the synagogue” since the text is referring to the synagogue that Aaron had entered (mentioned in verse 5); “their synagogue” implies that the Amlicites in the city of Jerusalem had only one synagogue, which was not the case.