Here we have one more instance of textual variation involving the subordinate conjunction that after “it came to pass” and before a prepositional phrase headed by in. As explained elsewhere, the that is generally optional in this context; see, for instance, under Alma 30:5 for the phrase “it came to pass (that) in the commencement of the Xth year” and under Mormon 1:8 for “it came to pass (that) in this year”. Here in Ether 11:12, the 1920 LDS edition added the that. However, this change was not marked in the committee copy for the 1920 edition, which suggests that this extra that was a typo. Since in general the that is optional after “it came to pass”, the critical text will follow the earliest text and restore the reading without the that here in Ether 11:12. Similarly, the that is lacking in Omni 1:20: “and it came to pass in the days of Mosiah there was a large stone brought unto him”.
Summary: Remove in Ether 11:12 the intrusive that (which was added apparently by mistake in the 1920 LDS edition), thus restoring the earliest reading: “and it came to pass in the days of Ethem there came many prophets”.