The evolution of Kaddish Yatom
Needless to say that Kaddish has always been one of the most important parts of communal prayers (see Brachot 3a, 21b). However neither Talmud Bavli nor Yerushlami associates Kaddish with a prayer intended to help the soul of the departed. Obviously there is nothing in Kaddish that mentions anything about the departed. Still the idea of a Kaddish recited by a Yatom definitely existed in the middle ages. In this short essay we will try to explore the earliest sources for the notion that Kaddish Yatom can help the soul of the deceased.
Bet Yosef on the Tur (Yore Deah 376) and Rema (ibid) bring various sources that are based on the following story: a sage meets some suffering man who tells him that he is dead and that he was wicked during lifetime. He will only be released from his suffering if his child will do various meritorious deeds. In some versions this individual does not have a child yet or is unsure if he has one, for when he died his wife was pregnant. The sage goes into trouble to find the wife and wait for her to give birth (or he finds a small child already, but that child is totally uneducated and wicked). The sage then teaches the child words of Torah and how to pray. Later on the child starts praying with congregation or teaches the Torah and the father comes to the sage (presumably in a dream) and thanks him for salvation.
The earliest three sources for this story that we still have are Masechet Kala Rabbati (second perek), Tana Debei Eliyahu Zuta (17), and Zohar Hadash (Rut and Parshat Achare Mot). Note that according to modern scholarship all three sources were composed later than Babylonian Talmud and therefore are not from Hazal but from Gaonic origin (Zohar Hadash may be even later). However much of the material they contain probably existed in the times of Hazal. However none of them except Zohar Hadash in Parshat Achare Mot mention Kaddish explicitly (and even there Kadish is mentioned together with Haftorah and prayer). Some mention that the child said Barchu or blessings in a congregation; others mention that he learned Torah.
Many early authorities bring variant versions of this Agada: Ohr Zarua (50), Orchot Chaim (Hilchot Avel), Kol Bo (114), Machzor Vitri (144), Rivash (115) and Menorat Hamaor (Perek Gidul Banim; he brings it from Midrash Tanchuma, Parshat Noach, but it’s not in our Tanchuma). Ohr Zarua actually mentions the word “Kaddish” in this story but he also mentions Barchu. He brings “Kaddish” in the name of Tana Debe Eliyahu (although in our Tana Debei Eliyahu it’s not “Kaddish” but “Barchu” that is mentioned). Machzor Vitri and Menorat Hamaor mention “Barchu”. Orchot Chaim, Kol Bo and Rivash mention both Kaddish and Haftorah.
What all of these versions of Agada have in common is that a son can save the father’s sinful soul if he performs some acts of merit. It would seem that the specific acts mentioned are the ones that a child could do. Indeed the Rema (ibid) rules that it is even better for the soul of the deceased that his son will be the Shliach Tzibur and this way he can add many merits, not just the Kaddish.
So where does the idea of Kaddish Yatom come from? It seems to me the main source is Kitvey Arizal (Shaar Kavonot, Drushei Kaddish, 1). Indeed the Sephardi mekubalim (e.g. Kaf Hachaim 55:20 and 132:17) understand Arizal to imply that there is a specific Kaddish during every prayer called “Kaddish Yatom” that is of greatest help to the soul of the departed.
Still those Sephardi poskim who don’t usually lean towards Kabbala, agree with Rema. For example, R. Ovadia Yosef writes (Yechave Daat 6:60, Yabia Omer Yore Deah 3:26) in the name of Yosef Ometz:
ויש להוסיף עוד לפמ"ש מהר"י יוזפא ביוסף אומץ (עמוד שלא), וז"ל, ענין הקדישים וברכו וכו' תיקון זה אינו רק לעמי הארץ, אבל לימוד תורה מועיל שבעתיים מכל התפלה וע"י כן מכניסין את המת לג"ע. ואם הבן מחדש חידושי תורה אין ערך להכבוד שזוכה אביו עי"ז בישיבה של מעלה. וכדמוכח במדרש הנעלם רות.
Kaddish and Barchu is mainly for uneducated but learning Torah helps seven times more than any prayer.
In conclusion we would like to say that while Kaddish Yatom became the most commonly associated Tikun for the dead, there are no early sources for this except Kitvey Arizal. So is there a source that Kaddish related is related to elevating the soul of the deceased? It depends on one’s opinion of Arizal. For those that think he had Ruach Hakodesh, indeed no other source is necessary.
 In most versions, it is Rabbi Akiva.
 R. Reuben Margolis interestingly states that the reason Haftorah specifically is mentioned is because of the Nusach of the blessing after it that is similar to Tziduk Hadin prayer during burial.
 Indeed a child can read the Haftorah (see Mishna Megila 4:6) and according to many opinions he can recite Kaddish as well (although some say that an adult should say together with him).
 In the Nusach Sepharadi it’s always the Kaddish before Alenu. It seems during Shacharit this is the Kaddish Derabonan after Pitum Haketoret (see Ben Ish Hai, Shana Rishona, Vayehi, 12 and Hagahot Ish Matzliach to siman 132) but Piske Tshuvot (132, note 77) understood it to be the Kaddish after Shir Shel Yom. Obviously in Nusach Ashkenaz, the Kaddish before Alenu is Kaddish Titkabal that is said by the Hazan and therefore the Rema brings the Kaddish Yatom to be the one after Alenu. During Mincha and Aravit Sephardim always recite a psalm before Alenu and afterwards Kaddish Yatom is recited, but no Kaddish is said after Alenu. Ashkenazim don’t say any psalm and consistency consider the Kaddish after Alenu to be Kaddish Yatom. As for the reason why this particular Kaddish helps the deceased soul, the Arizal states that this Kaddish is in the lowest world of Assya.
 The strong words Aruch Hashulchan (Yore Deah 376:12) that Kaddish Yatom is actually least meritorious contradict the words of Kaf Hachaim:
הקדיש הוא ענין גדול ובזה מזכים להמת הן להצילו מגיהנם והן להעלותו במעלות אך עקרי הקדישים הם מה שבתוך התפלה אבל קדישים שאחר עלינו ושיר של יום אינם אלא בשביל הקטנים אבל מי שיכול להתפלל לפני העמוד יגיד הקדישים שבתוך התפלה שהם העיקרים ושאחר התפלה יניח לקטנים ולא יגזול אותם ורבים מעמי הארץ טועים לומר דעיקר הקדיש הוא מה שאחר התפלה ונקרא קדיש יתום ואינם יודעים בין ימינם לשמאלם:
It’s possible that the author of Aruch Hashulchan did not see the exact quote from Kitvey Arizal.
 In the experience of present author with Jews from former Soviet Union, the majority of questions coming from middle age Jews are about Kaddish and Yizkor.
 Arizal is not the only authority who due to “Ruach Hakodesh” did not need to bring any “proofs” from the Talmud. Sefer Hassidim and Sheelot Utshuvot Min Hashamaim also bring no proofs for their rulings and are well quoted in Halachic literature.