In Avinu Malkeinu, we read, "חָנֵּנוּ וַעֲנֵנוּ כִּי אֵין בָּנוּ מַעֲשִׂים עֲשֵׂה עִמָּנוּ צְדָקָה וָחֶסֶד וְהוֹשִׁיעֵנוּ" be gracious with us and answer us, though we have no worthy deeds; treat us with charity and kindness and save us. (Translation from the Artscroll).
A similar sentence is used in tachanun on Mondays and Thursdays: אָבִינוּ מַלְכֵּנוּ חָנֵּנוּ וַעֲנֵנוּ. כִּי אֵין בָּנוּ מַעֲשים. צְדָקָה עֲשה עִמָּנוּ לְמַעַן שְׁמֶךָ
The final 5 words are also repeated later in tachanun.
I don't know a source for the phrase so I don't know if one is "more authentic" than another, but why would the two prayers use the same phrase but change the order of the words? One has asei imanu tzedaka and the other has tzedaka asei imanu. Is there a difference in meaning brought about by the shift in the words?