On weekday mornings, the Ashre preceding Uva Letzion is followed by Mizmor 20 (“Ya’ancha Hashem”). According to the Zohar HaHadash (Parashat Balak), this psalm has nine verses, which correspond to the nine months leading up to the final redemption during which the Mashiah will take suffering upon himself. Furthermore, there are seventy words, corresponding to the seventy ministers of each nation of the world, whom the Mashiah will vanquish. Rabbi Meir ben Gabai (Tola’at Yaakov, Sod Nefilat Apaim) writes that the nine verses and seventy words correlate with the nine months of pregnancy and the seventy cries a woman makes during contractions, respectively. Interestingly, he writes that a woman will not give birth until she has articulated seventy cries during her labor contractions. As well, the Mizmor has three hundred and ten letters, which correspond to the amount of spiritual worlds that Hashem created. This psalm was incorporated into the prayer because, as the Avudraham explains, it begins and ends with the words “Ya’ancha” and “Ya’anenu”, which convey the idea of Hashem answering our prayers.
The universal Sephardic custom is that Tahanun and Mizmor 20 are linked, such that on any day that Tahanun is omitted, this psalm is omitted as well. Conversely, the Rama writes (Orah Haim 131:1) that the Ashkenazic custom is that there are some days when Tahanun is omitted but the Mizmor is still recited, such when a groom is present.
Summary: Mizmor 20 has deep significance. The Sephardic custom is that on any weekday morning on which Tahanun is omitted, Mizmor 20 is omitted as well. It is auspicious to recite this psalm when a woman is in labor.