The term Atifa refers to covering of ones head during davening. The Rabbi’s deduced this requirement from verse, “Tefilla L’ani Ki Yatof”, although the term Tefilla is general for Shmona Esrei we nevertheless extend this obligation to everything that has the status of Dvarim Shebikdusha.
The Achronim quote a dispute from the Teshuvas Hageonim on whether or not the 13 middos of Selichos are considered to be Dvarim Shebikdusha or not. Nafka mina’s in this case would include whether or not people would have to stand as well as doing Atifa while reciting the 13 middos.
The only exception to this rule of Atifa is during the recital of Krias Shema. Although this is most definitely considered to be a davar shebikdusha, the Gemara (Brachos 10b) derives from the verse “Uvelechticha Baderech” that Shma may be said in an informal manner, thus eliminating the need to stand while reciting it, and according to R’ Chaim Soloveitchik this includes Atifa!
R’ Yosef Dov Soloveitchik held that the saying of Shema in an informal manner is not only permissible but is a complete fulfillment of “Koreh Kidarko”.
Therefore practically one should cover their head for Kadish before Barchu, remove the covering for Shema, and then cover their head again for Shmone Esrei.
* Nothing that is said in this post should be done LaMaisa without first discussing it w/ an official Rabbinic Authority.