Rabbi, What is the detail halakha of saying tzidkatkha?
Tzidkatcha is a compilation of three verses that are said after the chazan finishes chazara hashatz. It is only said on days that we would have said tachanun if it wouldn’t be shabbos. For example if Rosh chodesh is on Sunday, since we don’t say tachanun by mincha on erev Rosh Chodesh, therefore we wouldn’t say tzidkatcha on Shabbos either.
Shulchan Aruch Orach Chaim 292-2