When was the targum sheni second translation into Aramaic on Megillat Esther written?

There's no definitive answer to when the Targum Sheni (second translation) on Megillat Esther was written. Here's why:

* No Author or Date: Unlike other Targums, there's no clear author or date attributed to the Targum Sheni.

* Stylistic Evidence: Scholars use stylistic and linguistic analyses to try and determine the approximate time period. These analyses suggest a time range between the 6th to 10th centuries CE.

* Possible Influences: Some scholars point to possible influences from other Targums, Jewish legal texts, and even non-Jewish sources, adding further complexity to dating.

In summary, the exact date of the Targum Sheni is still a matter of scholarly debate, with a broad range of possibilities based on indirect evidence.