What were some of Samuel's duties as a boy priest?

Samuel was not a "priest" (kohen). He was a Levite (1 Chronicles ch.6); and the functions were not the same. The Levites assisted the Kohanim (Numbers ch.18). Their functions included singing at certain times in the Temple (Talmud, Berakhot 35a), carrying the Temple-vessels as needed (Numbers ch.3-4), guarding the Temple gates (Talmud, Tamid 27a), and other duties as needed.

They also served the nation as Torah-scholars (Deuteronomy 33:10).

In addition, Samuel served Eli (the kohen) as a personal manservant (1 Samuel 2:11).

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