During the reign of King Hezekiah, a highly organized administrative system was established to distribute offerings and tithes, ensuring the financial support of the Priests and Levites. This network carefully distinguished between those residing in their hometowns and those actively serving in the Temple. The primary approach among commentators is that the daily portions distributed in Jerusalem were given in addition to the standard allotments provided to the Priests in their local cities. However, another perspective suggests that this detail serves to separate the officials overseeing distribution in the priestly towns from the clerks managing the food supply for the Priests actively working in the Temple [מלבי״ם].
This distribution system relied on careful family registration, specifically linking fathers to the sons who accompanied them [רד״ק]. The family record focused downward, meaning the young sons were registered under their fathers and received their food strictly by virtue of their fathers' service [מלבי״ם]. The daily food allotments at the Temple were provided specifically to meet their everyday nutritional needs [מצודת דוד], but they were restricted to males from the age of three and older. Females were not included in this particular distribution because they did not take part in these specific visits to the sanctuary.
The minimum age requirement for boys was established because children under three lack the awareness necessary to keep their hands clean and are therefore not yet fit to enter the house of God. Once a boy reached the age of three, he could be properly trained to respect the holiness of the food and avoid defiling the sacred offerings through contact with impure things [רד״ק].
Importantly, the Priests did not receive these specific Temple allotments simply for visiting the sanctuary. They were only given this food when they arrived to perform their required duties during their officially scheduled shifts. During these designated periods of service, fathers made it a practice to bring their young sons along to educate them and accustom them to the holy work. Even though these boys were far too young to perform the Temple service themselves, the administrative system ensured they were fed from the sacrifices and sacred gifts while their fathers fulfilled their duties [מצודת דוד, מלבי״ם, ביאור שטיינזלץ].