Motzei Yom Kippur by Maariv one was Davening and in error said Hamelech Hakadosh instead of Hakeil Hakadosh and realized his error a bit later does he have to Daven over?
The Kaf Hachaim siman 117 siff 3 quotes a slew of achronim (yes, Ashkenazi ones like Elya Rabba) who say not to repeat shmoneh esrei. He brings a minority opinion that one may say Shmoneh esrei again as a nidava, but he suggests against this and says to rely on the majority opinion.
The seffer Shmaatsa di'Moshe in the back section called Shmuos Moshe quotes a kuntres Tefila Li'Moshe, that Reb Moshe Feinstein ruled that if someone said Hamelech Hakadosh on any other day of the year besides the aseres yomei tshuva he is not yotzeh and must repeat Shmona Esrei. His reasoning is that Ha'kel Hakadosh is a verse in Isaiah 5 and the nusach comes from there. Hamelech Hakadosh is not a passuk and therefore one is not yotzeh with this nusuch except during the ten days that it was niskan to be said.
The footnote there brings down the Aruch Hashulchan in siman 114 siff 11 who has a safeik if one is yotzei or not.
Qitzur Shulhhan Arukh, Yalqut Yosef (Orahh Hayim 624:2) states (my translation):
מי שטעה בתפלת ערבית של מוצאי יום הכפורים, ואמר המלך הקדוש או המלך המשפט, לדעת רוב האחרונים, יצא ידי חובת תפלה, והנכון שיחזור ויתפלל בתנאי של נדבה
One who erred during the 'Arvit prayer of Motza'ei Yom HaKippurim, and said "HaMelekh HaQadosh" or "HaMelekh HaMishpat", according to most Ahharonim one fulfilled one's duty to pray. Nevertheless, it is proper for one to repeat the prayer as a voluntary prayer.
NB: To my knowledge, Sefaradim (and perhaps other 'edot) permit voluntary prayers; but, Ashkenazim do not.
This OU site quotes halacha that says one need not go back and repeat.