Tzidkatcha (צדקתך, "Your righeousness") is a prayer consisting of group of three verses that is recited during the afternoon prayer on Shabbat. It is said in memory of three righteous individuals who died on Shabbat: Joseph, Moses and King David. It is recited at this prayer in particular because these individuals died in the afternoon.
Prayer content and meaning
The Bach asserts that Moses did not die in the afternoon of Shabbat but of Friday; however, he wasn't buried until Shabbat afternoon. Some say that the recital of this is to recall just judgement because it is immediately after Shabbat that sinners return to Gehinom.
The recitation of these verses represents our acceptance of God's judgment, referred to as Tziduk HaDin (צידוק הדין, "the righteousness of God's judgement"). It expresses the conviction that God is just in his actions, even when they are seemingly negative in human eyes. Because the time for afternoon prayers on Shabbat is near the closing of the day, the saddened atmosphere makes it appropriate for this prayer to be said. On days on which Tachanun would be omitted had it been a weekday, Tzidkatcha is omitted on Shabbat, as the added happiness of the day negates these feelings of sorrow.