Charles Ellicott Commentary 2 Chronicles 31:16

"besides them that were reckoned by genealogy of males, from three years old and upward, even every one that entered into the house of Jehovah, as the duty of every day required, for their service in their offices according to their courses;" — 2 Chronicles 31:16 (ASV)

Beside their genealogy. —The verse is a parenthesis stating an exception, and should instead be translated, “apart from their register of males from three years old and older (namely, the register) of all who came into the house of the LORD for the daily portion (literally, for a day’s matter in its day; 2 Chronicles 8:13; Nehemiah 11:23) for their service in their offices according to their divisions.” The meaning is that the Levites who were on duty in the Temple, and whose names were registered as such, along with their male children three years old and older, were not provided for by Cononiah and his associates, as they received their daily portion in the sanctuary itself. Children, it appears, were allowed to accompany their fathers to the Temple, and to eat with them from the sacrifices.