Question: Is there an issue to eat sharp or spicy foods on Rosh Hashanna?
Answer: We find mention in various sources, including the Chida in More B’etzba (Siman 254), that one should avoid eating sour foods on Rosh Hashana (the Chida mentions that one should refrain from eating lemons on Rosh Hashanna). The reason is because this is inauspicious on Rosh Hashanna.
The Mishna Berura (Siman 583 s.k. 5) also writes that there are those who refrain from cooking for Rosh Hashanna sour tasting foods. And regarding the second night of Rosh Hashanna the Mishna Berura (Siman 600 s.k. 4) also writes that one should not eat sour foods on Rosh Hashanna.
(The Mishna Berura also writes that in addition to the various foods that are eaten for a “good siman” at the beginning of the year, one should also be very careful not to become angry, because this is also not a “good siman”.)
There is also mention in other sources (Leket Yosher, Aruch Hashulchan) that one should avoid eating sharp foods on Rosh Hashanna.