Yishtabach
Tannaim and Amoraim
Yishtabach is one of the berakhot1 which is not found in the gemara. In the Manhig, הגהות מיימוניות, Tur and אבודרהם it says that Yishtabach is found in the Yerushalmi but it's not found in our text of Yerushalmi.
Geonim
The first mention of Yishtabach is in תשובות ר' נטרונאי גאון. The נוסח of Yishtabach in the siddurim of the Geonim in kind of similar to our נוסח with slight differences.
Rishonim
The Rishonim also have the נוסח of Yishtabach with slight differences. The Rambam has the berakha end with "ברוך אתה ה' א-להינו מלך העולם" as opposed to just "ברוך אתה ה'". It's possible that in the beginning the נוסח was "בא"ה אמ"ה" but since Yishtabach was a "ברכה הסמוכה לחברתה" they changed it to just "בא"ה".