The Torah is read during Shaharit on Tisha B’Ab, and this reading is followed by a Haftarah reading. The Shelishi – person who receives the third Aliyah – recites Kaddish after the Torah reading, before the Haftarah reading, just as is done at Shaharit on other days when there is a Haftarah. Hacham Matloub, in his Magen Ba’adi (Siman 14), writes that this was the custom in Halab (Aleppo, Syria).
We also read the Torah and a Haftarah at Minha on Tisha B’Ab, just as on other fast days, but Kaddish is not recited after the Torah reading. At Minha we follow the same protocol that is followed on other occasions when we have a Torah reading at Minha, namely, Shabbat and Yom Kippur. On all occasions when the Torah is read at Minha – Shabbat, Tisha B’Ab, Yom Kippur and other fast days – Kaddish is not recited after the Torah reading, regardless of whether or not a Haftarah is read.
Summary: On Tisha B’Ab, the person who receives the third Aliya to the Torah at Shaharit recites Kaddish after the Torah reading, before the Haftara. At Minha, however, Kaddish is not recited after the Torah reading.
