Mincha on Erev Shabbos
The Rema (550:3) rules that the Torah reading for a fast — “Vayacheil” — should be read in the Mincha of every fast day, even if it falls on a Friday. The Mishnah Berurah (550:11) adds that the chazan should also recite the additional prayer of aneinu in chazoras hashatz. However, being that it is erev Shabbos, tachanun and avinu malkeinu is omitted.
Rav Ovadia Yosef (Yechave Da’a 1:54) mentions that some communities recite avinu malkeinu even on Shabbos while omitting any phrases mentioning sin (such as the first avinu malkeinu). Sephardic Communities that follow this custom may certainly recite avinu malkeinu at Mincha of erev Shabbos.
People who have the custom to don tefillin for Mincha on a fast day should not do so this 10th of Teves. According to kabbalah [the secret facets of the Torah], tefillin should not be donned on erev Shabbos after midday. However, according to the revealed Torah there is no prohibition involved, and whoever has the custom to do so, may certainly go ahead and lay tefillin. One must, however, remove his tefillin before Shabbos.
