May one say Kaddish Yasom in the midst of Davening:
If one who generally says Kaddish is still in the midst of Davening [such as due to coming late, or due to Davening in length] and the congregation has reached the saying of Kaddish Yasom or Kaddish Derabanan, the question arises as to whether he may stop to say this Kaddish or not?
One who is not a Yasom [not within 11 months of a parents passing] may not make an interval to recite Kaddish Yasom/Derabanan within Davening starting from Baruch Shemara until after Shemoneh Esrei.
Pesukei Dezimra: One who is a Yasom [within 11 months of the passing of a parent] may stop to say Kaddish Yasom/Derabanan within Pesukei Dezimra. Some Poskim rule one may stop to do so even in the midst of a paragraph. Other Poskim however rule one may only do so between the paragraphs [Bein Haperakim]. [Practically, it is best to do so only between the paragraphs [Bein Haperakim].]
Birchas Shema: Some Poskim rule it may be recited even in middle of Birchas Shema [during Bein Haperakim]. Other Poskim rule one may not say Kaddish Yasom during Birchas Shema [even Bein Haperakim].
On the day of a Yartziet one follows the same law as a Yasom that is within 11 months of the passing of a parent.
 Pashut! See all Poskim listed below that the allowance is only for n Avel; See also Igros Kodesh 7/139 [printed in Shulchan Menachem 1/216]
 Rav Poalim O.C. 2/14; Alef Lamateh Dinei Kaddish Yasom 4/8 “So write Achronim and so is custom”; Yehuda Yaaleh 4; Sheilas Shalom 43; Maharshag 1/48; See Yabia Omer 7/10; See Kesher Gudal 7/35 that one may say the Kaddish before Hodu even after Baruch Sheamar
Other opinions: Some Poskim rule one may not recite Kaddish Yasom in the midst of Davening, past Baruch Sheamar, as Kaddish Yasom is only a custom and not a Halacha. [Levushei Mordechai 1/112; 2/36; Kaf Hachaim 53/13 that a Yasom may not stop to say Kaddish during Pesukei Dezimra as only the last Kaddish said before Aleiniu [Kaddish Derabanan].
 The reason: As it is permitted to make an interval during Pesukei Dezimra for the sake of answering for honor, and certainly in this case one may do so in which he is answering for his parent and fulfilling a Biblical command of Kibbud Av. [Rav Poalim ibid; Maharshag ibid; Yabia Omer ibid]
 Alef Lamateh Dinei Kaddish Yasom 4/8 writes one may say it between paragraphs, or between topics within a single paragraph.
 Rav Poalim ibid
 Sheilas Shalom 43; Implication of Rav Poalim ibid that it may be said in Bein Haperakim of Shema, as it has the same law as Bein Haperakim of Pesukei Dezimra regarding answering for Kavod.
 Alef Lamateh ibid strongly argues on the opinion of Sheilas Shalom ibid and says one is not to be lenient to recite it during Birchas Shema; The following Poskim prohibit even during Pesukei Dezimra: Levushei Mordechai 1/112; 2/36; Kaf Hachaim 53/13 that a Yasom may not stop to say Kaddish during Pesukei Dezimra as only the last Kaddish said before Aleiniu [after Shir Shel Yom]
 Alef Lamateh ibid