According to the Magen Avraham & MishnaVerurah. (565)
There is only one day in the year (YomKippur) that
the Piyut האדרת והאמונה ,לחי עולמים may be said בציבור
In Nusach Sfard (Ari) it is said every Shabbos.
They don't follow this Psak of the Magen Avraham/M.V.
Nusach Ashkenaz says it only on Yom Kippur
There are two* more things that are allowed to be done
only on Yom Kippur and not the rest of the year.
1) Standing up for קריאת שמע.
2) Saying י"ג מדות & סליחות in the night time before חצות
*that I could think of.- Saying aloud בשכמל"ו is done also during the year.