READING ACTS: What are the Testaments of the Twelve Patriarchs? (Phil Long). They are a second-century (Jewish-)Christian composition that draws more or less extensively, but also very freely, on Jewish sources in Aramaic and Hebrew. The history of research is complicated, but that's pretty much where the scholarly discussion is now.
One note. Please don't use the Greek Testament of Levi for Jewish background to the New Testament. It is a very free translation and adaptation of a Jewish work that we call Aramaic Levi. And we actually have substantial portions of Aramaic Levi from the Cairo Geniza and the Dead Sea Scrolls. Go straight to the source and use Aramaic Levi.
I have published an English translation of Aramaic Levi in in Old Testament Pseudepigrapha: More Noncanonical Scriptures, volume 1 (ed. Bauckham, Davila, and Panayotov; Eerdmans, 2013), pp. 121-142. It is a translation of my own eclectic reconstruction of the text based on all of the surviving fragments. The introduction also discusses the relationship between Greek Testament of Levi and Aramaic Levi in greater detail.
I have posted some related comments here. For past posts in Phil Long's blog series on the OTP, see here and links.
