Re – question 1640 in regards to someone who became a diabetic and cannot fast anymore reciting Aneinu, we wrote that Horav Shlomo Miller’s Shlit’a opinion is that one can still say Aneinu, but omit the phrase “beyom tzom taanisenu.
Q. In that case, may I also get an Aliyah on a Ta’anis?

A. Horav Shlomo Miller’s Shlit’a opinion is that one that does not fast should not be called to the Torah as the Mishna Berura (566: 21) rules. And even if he is the only cohen he should exit at that time. The fact that one can recite Aneinu when omitting “beyom tzom taanisenu,” is because it is only an elaboration and expansion to a tefila, that one may voluntarily add when true. (See similar opinion in Piskei Teshuvos (566: n. 28).
The Rov commented that you may get an aliya on a taanis during shacharis, but try to daven early and be still fasting.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a