1. a. On every fast day three people are called to the Torah at Shaharit, and three are called at Minhah.

b. Only people who are fasting may receive an aliyah. Even if a person is the only Kohen present he still may not receive the first aliyah (belonging to the Kohen) if he is not fasting. A Yisrael replaces the Kohen preceded by the announcement of אין כאן כהן יעמוד ישראל במקום כהן. A Levi should not be called up for the next two aliyot.

Similarly, a Levi who is not fasting may not receive the second aliyah, even if he is the only Levi present. The same Kohen who was called for his own aliyah is called again to replace the Levi.

c. If the non-fasting Kohen or Levi are the only Kohen or Levi present, they should leave the Sanctuary before their aliyah. Even if his name was called he should refuse the aliyah and explain that since he is not fasting he can not receive an aliyah.

d. If the fast falls on a Monday or Thursday, days that we always read the Torah, then if the non-fasting Kohen or Levi was publicly called at Shaharit by name he should accept the aliyah. However, if he was asked privately he should refuse. 

2. An individual who knows he will not complete the fast should not accept an aliyah, even if he has not yet eaten.

3. The ba’al Koreh, Torah reader, should not read the Torah for the congregation if he is not fasting. However, if no one else can replace him it is permissible to be lenient and permit him to read.  

4. It is our custom not to recite a Haftorah on a fast day, except on Tishah B’Av at Shaharit; unlike the Ashkenazim who recite a Haftorah on every fast. Therefore, a Sephardi who prays at an Ashkenazi synagogue should not accept the third aliyah (which is maftir) because it is not his custom to have a Haftorah and the third aliyah would obligate him to make the berachot for the Haftorah. However, if they already publicly called his name for the third aliyah, he should go up and recite the berachot of maftir. 

5. a. There must be at least six people fasting in the congregation in order to read the Torah portion.

b. If there are less than six people fasting present in the congregation then the Sefer Torah is not read.

c. When the fast falls on a Monday or Thursday and there are less than six people present who are fasting, by Shaharit we read the parshah of the week and not the special reading for the fast day.