אורח חיים קכ״וOrach Chayim 126

Se’if 1א׳

שְׁלִיחַ צִבּוּר שֶׁטָּעָה וְדִלֵּג אַחַת מִכָּל הַבְּרָכוֹת, וּכְשֶׁמַּזְכִּירִין אוֹתוֹ יוֹדֵעַ לַחֲזֹר לִמְקוֹמוֹ, אֵין מְסַלְּקִין אוֹתוֹ; אֲבָל אִם דִּלֵּג בִּרְכַּת הַמַּלְשִׁינִים, מְסַלְּקִין אוֹתוֹ מִיָּד, שֶׁמָּא אֶפִּיקוֹרוֹס הוּא; וְאִם הִתְחִיל בָּהּ וְטָעָה, אֵין מְסַלְּקִין אוֹתוֹ.

The Laws of a Prayer Leader Who Erred. Containing 4 S'ifim: A prayer leader who erred and skipped one of the blessings [of the Amidah], but when they reminded [the leader] of it, [the leader] knows to which place to return [in the prayer], they need not remove [the leader from leading]. If, however, [the leader] skipped the "Blessing Concerning the Heretics" ["al ha-Malshinim"], they remove [that leader] immediately because perhaps [the leader] is a heretic [Apikorus]. But if [the leader] began [that blessing] and [then] erred, we do not remove [the leader].

Se’if 2ב׳

שְׁלִיחַ צִבּוּר שֶׁטָּעָה וְאֵינוֹ יוֹדֵעַ לַחֲזֹר לִמְקוֹמוֹ, יַעֲמֹד אַחֵר תַּחְתָּיו (כְּדֶרֶךְ שֶׁנִּתְבָּאֵר לְעֵיל סי' נ"ג), וּמַתְחִיל מִתְּחִלַּת הַבְּרָכָה שֶׁטָּעָה זֶה, אִם הָיָה הַטָּעוּת בָּאֶמְצָעִיּוֹת; וְאִם הָיָה בְּג' רִאשׁוֹנוֹת, מַתְחִיל בְּרֹאשׁ; וְאִם בְּג' אַחֲרוֹנוֹת, מַתְחִיל רְצֵה.

If a prayer leader erred and does not know to which place to return [in the Amidah], another person should replace [the original leader] (in the manner that was explained above in siman 13). And [the replacement] begins from the beginning of the blessing [where the error occurred]. This is if the erring was in [one of] the middle [blessings], but if [the error] was in one of the first three [blessings], [the replacement] begins from the start [of Amidah]. And if [the error was] in [one of] the latter three [blessings], [the replacement] must begin with [the blessing of] Retzei [the beginning of the latter three].

Se’if 3ג׳

כָּל מָקוֹם שֶׁהַיָּחִיד חוֹזֵר וּמִתְפַּלֵּל, שְׁלִיחַ צִבּוּר חוֹזֵר וּמִתְפַּלֵּל, אִם טָעָה כְּמוֹתוֹ כְּשֶׁמִּתְפַּלֵּל בְּקוֹל רָם, חוּץ מִשַּׁחֲרִית שֶׁל רֹאשׁ חֹדֶשׁ, שֶׁאִם שָׁכַח שְׁלִיחַ צִבּוּר וְלֹא הִזְכִּיר יַעֲלֶה וְיָבֹא עַד שֶׁהִשְׁלִים תְּפִלָּתוֹ, אֵין מַחֲזִירִין אוֹתוֹ, מִפְּנֵי טֹרַח הַצִּבּוּר, שֶׁהֲרֵי תְּפִלַּת הַמּוּסָפִין לְפָנָיו שֶׁהוּא מַזְכִּיר בָּהּ רֹאשׁ חֹדֶשׁ; אֲבָל אִם נִזְכַּר קֹדֶם שֶׁהִשְׁלִים תְּפִלָּתוֹ, חוֹזֵר לִרְצֵה וְאֵין בָּזֶה טֹרַח צִבּוּר. הַגָּה: יֵשׁ אוֹמְרִים דְּאִם טָעָה בְּשַׁחֲרִית שֶׁל שַׁבָּת וְיוֹם טוֹב, דִּינוֹ כְּמוֹ בְּרֹאשׁ חֹדֶשׁ, וְהָכֵי נָהוּג (טוּר וּסְמַ"ק).

In any case in which an individual goes back and prays [the individual Amidah again due to a mistake], [so too] a prayer leader goes back and prays [again] if [the prayer leader] erred in like manner when praying [the Amidah] aloud - except for Shacharit of Rosh Chodesh - since if the prayer leader forgot and did not realize [and recite] Ya-aleh V'yavo before [the leader] finished [the leader's] prayer [i.e. Amidah], We do not require [the leader] to go back [and repeat the Amidah again], because this would be a burden for the congregation since after all, the Musaf prayer is still to come and in which [the prayer leader] mentions Rosh Chodesh. But if it was remembered before [the leader] concluded [the leader's] prayer, [the leader] goes back to [the blessing of] Retzei and it is not considered a burden for the congregation. Gloss: There are those who say that if [the leader] made a mistake in Shacharit of Shabbat, or of Yom Tov, the rule is the same as Rosh Chodesh, and this is how we practice (Tur and Sefer Mitzvot Katan])