Artscroll English Siddur has in the על הנסים the word as חַשְׁמוֹנַאי. The Artscroll all Hebrew Siddur has the word as חַשְׁמוֹנָאִי. Which is correct? Is there a difference in meaning if it is חַשְׁמוֹנָאִי or חַשְׁמוֹנַאי?
I found this answer from Yehuda Marks.
He says that Rabbi Zalman Henna held that the correct pronunciation was חַשְׁמוֹנַאי while Rabbi Yaakov Emden held the correct pronunciation was חַשְׁמוֹנָאִי.
He says the Sefardim also have a disagreement as to the correct pronunciation. The Pri Chadash, Ben Ish Chai and Harav Meir Mazuz rule that the correct way of saying the word is חַשְׁמוֹנָאִי, while the Zivchei Tzedek and Harav Ovadia Yosef state that the correct pronunciation is חַשְׁמוֹנַאי.
He also quotes Rav Shaul Yeshua Abutbul of Morocco (quoted in Ramat Shmuel 135) arguing that the suffix ָאִי is not used in lashon hakodesh, only in targum. Instead, חַשְׁמוֹנַאי is the name of another person, as in יַנַאי, i.e. In the days of Matisyahu ben Yochanan Cohen Gadol, and Chashmonai and his children.
There is a machlokes as to how the word חשמונאי is pronounced. While Reb Zalman Henna writes that the word should be voweled with a pasach under the nun and pronouncedחַשְׁמוֹנַאי , with a silent aleph, Harav Yaakov Emden, in his siddur Beis Yaakov and elaborated in his Luach Eress, strongly disagrees, ruling that the word should be voweled with a kametz under the nun and a chirik under the aleph, חַשְׁמוֹנָאִי, and this is the accepted pronunciation in the Ashkenaz siddurim. One of Rav Emden’s arguments is that if the aleph isn’t pronounced, why is it there? He comments that even the Sephardim pronounce the word חַשְׁמוֹנָאִי. But that is not so clear-cut, since there is a machlokes amongst the Sephardim over the word. While the Pri Chadash Ben Ish Chai and Harav Meir Mazuz rule that the correct spelling is חַשְׁמוֹנָאִי, The Zivchei Tzedek and Harav Ovadia Yosef state that the better pronouncing is חַשְׁמוֹנַאי, with a pasach and skipping the aleph, with the Zivchei Tzedek stating that this is the minhag of the chazanim in Baghdad. Rav Shaul Yeshua Abutbul of Morocco (quoted in Ramat Shmuel 135) argues that the suffix ָאִי is not used in lashon hakodesh, only in targum. Instead, חַשְׁמוֹנַאי is the name of another person, as in יַנַאי, i.e. In the days of Matisyahu ben Yochanan Cohen Gadol, and Chashmonai and his children. (This view can be supported by the gemara Megillah 11a and Maseches Sofrim 20:8). However, Rav Emden disagrees with this proof, saying that we do find the suffix ָאִי in Lashon Hakodesh, as in the word אַכְזָרִי, especially according to the Redak who says the word comes from the root חשמן, as in יֶאֱתָיוּ חַשְׁמַנִּים (Tehillim 68:32), meaning an honourable person.