I have noticed in some siddurim that there are pesukim interspersed before kaddish and between sections from תתקבַל onwards. For those unaware of this practice, it may be found on pg. 58 of this edition of the Siddur Sefat Emet printed for the French community.
While I have heard that these additions post-date the Rishonim, I have heard this without a source. What is the source of these additions?