From where does the Chabad melody that is customarily sung by the priestly blessing, come from?

It originated from the choir of the Mittler Rebbe. Interestingly, the Rebbe Rayatz testifies that he heard it for the first time while he was in the city of Riga, in the 1930s. From here we can understand that it was not traditionally sung in Lubavitch, and while perhaps it was composed by the choir or a member of the choir, it never became the official tradition until later.

Likkutei dibburim vol. 3 likkut 23:72 p. 624