The tradition of eating cheese on Hanukah pre-dates latkes, sufganiyot and other more modern traditions.
The story is the stuff of a Hollywood drama. Judith, a beautiful Jewish woman fed salty cheese to Nebuchadnezzar, king of the Assyrians general Holofernes. The cheese made him thirsty and he drank too much wine which caused him to fall into a drunken sleep. Judith cut off his head and the Israelis rallied and attacked the Assyrian armies who then fled.
One version of the story specifies that the cheese was cooked into a pancake. By the 14th century, there's quite a strong tradition that people eat cheese on Hanukkah and it’s associated with Judith giving cheese to the enemy to make him drunk.
A commentary from that time, by Rabbi Moses Isserles, on the Shulchran Arach, the Jewish Code of Law, even recommends eating cheese on the holiday in honor of Judith.
The latke that we know today is actually a modern recipe. The potato, after all, didn't come to Europe until well after Columbus came to America. Potato latkes were a 19th-century invention. The tradition of eating cakes made from cheese on Hanukkah died out when European Jews cooked in schmaltz.
Eating cheese during Hanukkah is a very old tradition that still continues today. Many people have forgotten why we eat dairy products. Here is a delicious recipe that honors Judith and her bravery, Feta Cheese Fritters with Zucchini and Potato.
Chag Hanukkah Sameach!