What should one do if he notices that his kippah fell off during the Amidah?
How does this depend on whether he is between brachot, in the middle of the body of a bracha, or saying the bracha itself?
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The classical case cited in halachic sources is a siddur falling (see e.g., Kitzur Shulchan Aruch 18:9)
R Eliezer Melamed writes (Peninei Halacha Hilchot Tefila 17:15) that one is permitted to interrupt his Amidah to fix a problem only if it will bother him so much that he cannot concentrate, and it should be done between the brachot.
If during the Amidah, a problem occurs that if not fixed immediately will cause him damage, he is not permitted to interrupt his prayer (Mishnah Berurah 104:2; Kaf HaChaim 6). However, if the matter bothers him so much that he cannot concentrate, he is permitted to attend to the problem.
If a siddur falls to the floor and the person reciting the Amidah cannot concentrate until it is picked up, he must first finish the berachah that he is saying, and then he may go pick it up.
However, unlike with a siddur, there is an obligation to cover once head when praying (SA OC 91:3, MT Tefila 5:5). Regarding someone who prays without a kippa by mistake and notices afterward, many halachic decisors rule he doesn't have to repeat his prayer (although some rule strictly, see here).
Based on the above, I discussed various scenarios with R Binyamin Tabady and he ruled that
And if you want more on the topic, see R Ari Wasserman's ultimate encyclopedia of all kippa-related questions: Otzar Ha-Kipah: Kipos, Kovim Ve-Atifas Ha-Rosh as well as his shiur on the topic at YUTorah (also mentioned by ezra in his answer on this page).
If one's yarmulke fell off during the amidah it is muttar for him to pick it up and even to walk a few steps to do so. If someone is mapkid to wear two coverings if his hat blew off he is allowed to pick it up again between brachos if it causes him to lose kavanah. This is similar to the case of a siddur dropped during the amidah as brought forth in the other answer here. I learned all this from Rabbi Ari Wasserman in his 5 min shiur here