Is Kaddish recited for a child who passed away below Bar Mitzvah?
Some Poskim rule the Kaddish is not to be recited for a deceased child until he reaches the age of mitzvah’s which is 12 years old her girl and 13 years old for a boy, and so is the custom of some communities. Other Poskim however rule that Kaddish is to be recited even on behalf of a child below the age of mitzvah’s, and so is the main ruling and so was the directive of the Rebbe in negation of the previous practice.
From what age? Some Poskim rule that Kaddish is only said from the time the child reaches the age of Chinuch. Other Poskim hold that it is said from the age of one years old. Other Poskim rule that Kaddish is to be said if the deceased child was over 30 days old and so is the Rebbe’s opinion, and so is the final ruling and widespread practice to recite Kaddish on behalf of a child of any age who passed away r”l, as long as the child was over 30 days old.
Who is to say the Kaddish? It is best for the father of the child to recite Kaddish for his son or daughter if the father’s parents are not alive. If his parents are alive, then he is not to say Kaddish and rather another person is to be hired to do so, unless his parents are Mochel. [Nevertheless, some are accustomed that a father never says Kaddish on behalf of his child. Practically, the son is not to say Kaddish if both of his parents are alive, even if they are Mochel.]
 See Tzitz Eliezer 7:86-7; Nitei Gavriel 40:6; Igros Kodesh 19:44 [published in Shulchan Menachem 5:306]
Other opinions: Some write that the custom is not to say Kaddish on behalf of a child below 13 years of age. [Sefarim brought in Igros Kodesh ibid] On a related issue, see Rav Akiva Eiger 384 in name of Chidushei Gershoni that if a child who was less than one year of age passed away, one is not to make a Minyan in his house during the Shiva.
 Maaseh Avraham Y.D. 59 regarding custom in Izmir; Letter of Rav Pesach Tzevi Frank in Sefer Hakaddish and Yalkut Das Vadin of Rav Asaf p. 70; See Noda Beyehuda Tinyana 8, brought in Pischeiy Teshuvah 376:3; Sdei Chemed 212 in name of Ikarei Hadat Y.D. 36:11 that some places don’t say Hashkava on child less than Bar and Bas Mitzvah
 Michaber 344:4 and Shach 344:3 regarding Kaddish of Tziduk Hadin that is said from 30 days; Rama 344:4 regarding Kaddish and Tziduk Hadin by funeral that it is said for child over 12 months; Sdei Chemed Aveilus 151, 162, 212; Mishmeres Shalom Kuf Samech; Kol Bo Grennwald 5:1-20; Igros Kodesh 19:44 [published in Shulchan Menachem 5:306] that the same applies throughout the year; Tzitz Eliezer 7:86-7; Gesher Hachaim 1:118; Pnei Baruch 34:30; Yabia Omer 9 Y.D. 36
 Sdei Chemed Aveilus 151, 162, 212; Gesher Hachaim 1:118; Sefer Hakkadish p. 181 as main opinion; Pnei Baruch 34:30 as main opinion
 See Rama 344:4 regarding Kaddish and Tziduk Hadin by funeral that it is not said for under 12 months; See Maaseh Avraham Y.D. 59 regarding custom in Tzefas
 Michaber 344:4 and Shach 344:3 regarding Kaddish of Tziduk Hadin; Vayitzbar Yosef 21; Hillel Omer 231; Gesher Hachaim 2:12 that so is Minhag Yerushalayim; Sefer Hakkadish p. 181 as second opinion; Pnei Baruch 34:30 as second opinion; Tzitz Eliezer 7:86-7; Nitei Gavriel ibid and footnote 10 that so is the custom and that so is the custom of Chabad and Ashkenaz; Yabia Omer 9 Y.D. 36
 Igros Kodesh 19:44 [published in Shulchan Menachem 5:306]
 The reason: As although a child is not held responsible for wronging, nevertheless, there are many benefits of Kaddish asides for removing him from Gehinnom. See also Noda Beyehuda ibid that a child is punished for wrongdoing.
 See next Q&A
 Ruling of Rav Yaakov Landa heard from his son, Rav Eli Landa; Rav Zalman Shimon Dworkin, as related by Rav Groner; Maaseh of Rav Avraham Tzvi Hakohen, who did not say Kaddish for his 18 month old son who passed away; See Hiskashrus 644:16 and 649 and 682
 Nitei Gavriel 2:43 footnote 6 in name of Rebbe; 49:2