The order of the Siyum-Kaddish and Asara Bnei Rav Papa:[1]

After completing the final lines of the Misechta during the Siyum celebration, Kaddish Derabanan is to be recited if a Minyan is present. One is to strive to have a Minyan by the Siyum in order to say this Kaddish. The prayer of [Hadran Alach and] Asara Bnei Rav Papa is recited [before the Kaddish].[2] [Other prayers are also customarily added, including a prayer within the Kaddish Hagadol. The Chabad custom is to recite the regular Hadran Alach, Aseres Bnei Rav Papa, and then go straight to a regular Kaddish Derabanan.[3]]

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[1] Shach 246/27 in name of Mahram Mintz 2/119;

[2] Shach ibid; Maharam Mintz 2/119; Teshuvas Harama in end; Rashal in Yam Shel Shlomo Bava Kama 37; Rav Haiy Gaon, brought in Sefer Haeshkol

The reason: Some suggests that Rav Papa was wealthy, and was accustomed to make a large Siyum for his sons when they would complete a Misechta. The ten sons also correspond to the ten utterances with which the world was created. [Rama ibid] Alternatively, the sons of Rav Papa are mentioned because they all passed away Al Kiddush Hashem during the lifetime of their father, and hence we mention their name Leiluiy Nishmas. [Zecher Yehoseif on Miseches Brachos]

[3] Reshimos Devarim of Rav Chitrik 4/219; Directive of Rebbe to Rav Binyamon Althouse; Toras Menachem 4/239 that the Rebbe remarked to Rav Meir Ashkenazi who said the long Kaddish “This is a novelty to me, and I have never seen this done beforehand.”; See also Hisvadyus 5745 3/1700