When Yom Kippur falls on Shabbos, are we supposed to fast? If we did & weren't suppose to, how do we fix it?

Shalom, Thank you for your question. Yom Kippur is called in the Torah (Lev. 16:31) "Shabbat Shabbaton", that is "The Shabath of the Shabaths". From this we learn that it's holiness is even greater than a regular Shabbat. Therefore we fast on Yom Kippur even when it falls out on Shabbat. (All the other fasts are moved if they fall on Shabbat). Blessings