(לא) וְהִקְטִ֧יר הַכֹּהֵ֛ן אֶת־הַחֵ֖לֶב הַמִּזְבֵּ֑חָה וְהָיָה֙ הֶֽחָזֶ֔ה לְאַהֲרֹ֖ן וּלְבָנָֽיו׃ (לב) וְאֵת֙ שׁ֣וֹק הַיָּמִ֔ין תִּתְּנ֥וּ תְרוּמָ֖ה לַכֹּהֵ֑ן מִזִּבְחֵ֖י שַׁלְמֵיכֶֽם׃ (לג) הַמַּקְרִ֞יב אֶת־דַּ֧ם הַשְּׁלָמִ֛ים וְאֶת־הַחֵ֖לֶב מִבְּנֵ֣י אַהֲרֹ֑ן ל֧וֹ תִהְיֶ֛ה שׁ֥וֹק הַיָּמִ֖ין לְמָנָֽה׃ (לד) כִּי֩ אֶת־חֲזֵ֨ה הַתְּנוּפָ֜ה וְאֵ֣ת ׀ שׁ֣וֹק הַתְּרוּמָ֗ה לָקַ֙חְתִּי֙ מֵאֵ֣ת בְּנֵֽי־יִשְׂרָאֵ֔ל מִזִּבְחֵ֖י שַׁלְמֵיהֶ֑ם וָאֶתֵּ֣ן אֹ֠תָם לְאַהֲרֹ֨ן הַכֹּהֵ֤ן וּלְבָנָיו֙ לְחָק־עוֹלָ֔ם מֵאֵ֖ת בְּנֵ֥י יִשְׂרָאֵֽל
(31) the priest shall turn the fat into smoke on the altar, and the breast shall go to Aaron and his sons. (32) And the right thigh from your sacrifices of well-being you shall present to the priest as a gift; (33) he from among Aaron’s sons who offers the blood and the fat of the offering of well-being shall get the right thigh as his portion. (34) For I have taken the breast of elevation offering and the thigh of gift offering from the Israelites, from their sacrifices of well-being, and given them to Aaron the priest and to his sons as their due from the Israelites for all time.
MISHNA: The thanks offering and nazirite’s ram are offerings of lesser sanctity...they are eaten throughout the city of Jerusalem, by every person, i.e., any ritually pure Jew, prepared in any manner of food preparation, on the day the offering was sacrificed and during the night that follows, until midnight. The status of the portion that is separated from them and given to the priests is similar to theirs; but the portion that is separated is eaten by the priests, by their spouses, and by their sons, and by their servants.
The verse in Parshat Tzav is explicit that the children of the kohanim receive the meat as well. Why does the mishnah have to specify this fact?
Sefat Emet Al HaShas, Zevachim 55a
This is confusing; what is the meaning of "and by their sons" in the mishnah? What does it matter whether its the father or the son - they are both kohanim [and therefore can eat from the sacrifice!]....Perhaps one may have thought that the eating of sacrifices is a form of avodah, holy service, and as such children should not eat of it, as they are not fit for avodah yet. Therefore the mishan comes to teach us that they nevertheless may eat from the sacrifice.

R. Ari Storch, Tiferet Aryeh...It seems that the mishnah taught "and their children" to teach us that its possible for the kohein to give the breast and the thigh to the children, and even young children. For I would have thought that its prohibited to give them to young children, as we understand from elsewhere that sacrificial meat must be eaten b'derech kavod, in an honorable fashion. Therefore the mishnah explains that we do not need to give the kohanic gifts to a particularly honored individual, but rather anyone can eat in and it still be considered kavod.
