At my shul (a sephardi one), I occasionally see people wearing tefillin at mincha on fast days (other than Tisha b'Av). Is this a minhag with a source, or is there some other reason why people do this?
Rabbi Maroof attributes this to the Beis Yosef (he doesn't give an exact citation).
He lists three reasons why.
1) To help reach 100 blessings for the day.
2) Increased spiritual awareness on a fast day allows one to increase the amount of time in a day that Tefillin is worn.
3) Wearing Tefillin focuses concentration during prayer.