- Peninei Halakha
Throughout the year, Birkat Kohanim is not performed at Minĥa as it is at Shaĥarit (according to Ashkenazic custom in Eretz Yisrael and according to Sephardic custom worldwide), because people usually eat a meal before Minĥa, and we are concerned that the Kohanim might bless the people while under the influence of alcohol, which is forbidden. On fast days that have a Ne’ila service, like Yom Kippur and the fasts that the Sages instituted for droughts, the Kohanim bless the people at Ne’ila, because there is no reason to be concerned that they will be drunk, as it is a fast day. During Minĥa of those days, however, the Kohanim do not bless the people, out of concern that they may mistakenly think that they may do so on regular days as well. On ordinary fast days, when we do not pray Ne’ila, the law depends on when the congregants pray Minĥa. If a congregation that recites Birkat Kohanim prays Minĥa at the same time that Ne’ila would take place, i.e., shortly before shki’a, the Kohanim bless the people (cf. Ta’anit 26b; sa 129:1). But if the congregation prays Minĥa earlier, Birkat Kohanim is omitted, since it is not the time designated for Ne’ila. In such a case, the ĥazan also omits “Elokeinu Ve-Elokei Avoteinu,” which is customarily recited when no Kohanim are present.
Therefore, it is proper for congregations that recite Birkat Kohanim to schedule Minĥa on fast days for a time that enables people to participate in the mitzva of Birkat Kohanim. Ideally, one should pray Minĥa within half an hour of shki’a, which is the best time to pray Ne’ila. Nevertheless, as long as the congregation prays after plag ha-minĥa (one and a quarter seasonal hours before the end of the day; see n. 16), the Kohanim may bless the people. If they pray earlier than that, however, Birkat Kohanim is omitted.
A Kohen who is not fasting should not perform Birkat Kohanim. If there are no other Kohanim present, some maintain that he still may not perform the mitzva (Kaf Ha-ĥayim 129:5), while others maintain that he should. The latter opinion goes as far as to say that he should perform it even if there is one other Kohen (Lu’aĥ Eretz Yisrael; Halikhot Shlomo, Tefila 10:13). If there are fewer than six people fasting, no Kohen should perform the blessing at Minĥa, even if he is fasting (see Piskei Teshuvot 129:2).
 According to Ginat Veradim, a Kohen who is not fasting may nonetheless perform Birkat Kohanim at Minĥa of a fast day in congregations that recite Birkat Kohanim, because there is no concern that he will perform the blessing while drunk on a fast day. All other poskim disagree. According to Ĥazon Ish, oĥ 20, Kohanim may perform the mitzva even when praying an early Minĥa, as there is no concern that they will be drunk. However, most poskim maintain that Birkat Kohanim is recited only when praying Minĥa at the time of Ne’ila, which is close to shki’a. Rav Pe’alim oĥ 5, Kaf Ha-ĥayim 129:7, Lu’aĥ Eretz Yisrael (by R. Yeĥiel Michel Tikochinsky), Piskei Teshuvot 129:1 all maintain this view. The basis for this opinion is the fact that the Kohanim do not bless the people at Minĥa of Yom Kippur, as the Sages were concerned that they might mistakenly do so on a regular day. The reason they were concerned is that Minĥa can be prayed on Yom Kippur at the same time we pray Minĥa on a regular day. Furthermore, the earliest time for Minĥa is close to midday, which is when people eat lunch and are liable to drink wine, as opposed to Ne’ila, which is said at the end of the day. Therefore, on a day that has no Ne’ila service, the Kohanim bless the people during Minĥa in congregations that recite Birkat Kohanim only if it is said at the time of Ne’ila. Nonetheless, everyone agrees that if the Kohanim ascended the platform to perform the mitzva during a Minĥa service that is being held before plag ha-minĥa, they may continue. Many authorities rule this way with regard to Minĥa of Yom Kippur. Plag ha-minĥa is 1.25 seasonal hours before the end of the day. There is a dispute whether “the end of the day” refers to shki’a or tzeit ha-kokhavim; see Peninei Halakha: Prayer, ch. 24 n. 9. For our purposes here, we calculate plag from shki’a, as explained there, ch. 20, n. 3. Le-khatĥila, it is best to schedule Minĥa such that the congregation will recite the Amida half an hour before shki’a, as this is the proper time, le-khatĥila, for Ne’ila.
Be-di’avad, if the ĥazan’s repetition of the Amida extends past shki’a, the Kohanim may perform the mitzva up until tzeit ha-kokhavim, as there is a combination of uncertainties here: 1) According to Raavya, Yere’im, and Or Zaru’a, Kohanim may perform the blessing at night; 2) the status of bein ha-shmashot is uncertain, and it may be considered daytime; 3) according to Rabbeinu Tam, the period following shki’a is definitely daytime. sah 623:8 and Piskei Teshuvot 623:13, quoting R. Shlomo Zalman Auerbach and R. Yosef Shalom Elyashiv, both rule accordingly. Yeĥaveh Da’at 6:40 and Or Le-Tziyon 2:8:13 concur, adding that this period lasts for 13.5 minutes following shki’a.