Many yiden have the custom to eat potato latkes or jelly doughnuts on chanukah. Who started this custom??
Wikipedia brings the following quote from Rabbi Maimon, father of the Rambam:
"אין להקל בשום מנהג ואפילו מנהג קל. ויתחייב כל נכון לו עשות משתה ושמחה ומאכל, לפרסם הנס שעשה השם יתברך עמנו באותם הימים. ופשט המנהג לעשות סופגנין, בערבי אלספינג, והם הצפחיות בדבש, ובתרגום: האיסקריטין, והוא מנהג הקדמונים משום שהם קלויים בשמן, זכר לברכתו"
Admittingly, though, he may be talking about the sfenj which is more common by Sephardic communities. But the point is, that he says that it's a minhag that was started by the ancients, long ago.*
On latkes, Rabbi Dr. Chaim Simons traced the origins of eating latkes or levivot in Hebrew, in an essay in Hebrew titled "The consumption of cheese and levivot on Chanukah". In it he says that a 1402 manuscript of Sefer Yehudit says that one of the foods that Yehudit fed the Greek ruler were levivot. Levivot are first mentioned in the story of Amnon and Tamar:
"וַיִּשְׁכַּ֥ב אַמְנ֖וֹן וַיִּתְחָ֑ל וַיָּבֹ֨א הַמֶּ֜לֶךְ לִרְאֹת֗וֹ וַיֹּ֨אמֶר אַמְנ֤וֹן אֶל־הַמֶּ֙לֶךְ֙ תָּֽבוֹא־נָ֞א תָּמָ֣ר אֲחֹתִ֗י וּתְלַבֵּ֤ב לְעֵינַי֙ שְׁתֵּ֣י לְבִב֔וֹת וְאֶבְרֶ֖ה מִיָּדָֽהּ׃
Amnon lay down and pretended to be sick. The king came to see him, and Amnon said to the king, “Let my sister Tamar come and prepare a couple of cakes in front of me, and let her bring them to me.”"
On the word "ותלבב", Rashi writes:
"ותלבב. ותחלוט, סולת מורבכת במים רותחין תחלה, ואחר כך בשמן:
She made a paste. She made a paste of flour mixed [it] first into boiling water and afterwords in oil." (Rashi Shmuel 2:13:8)
Metzudat David writes:
"ותבשל. עוד פעם על המחבת בשמן:
Once more on the pan with oil." (Metuzdat David, Shmuel 2:13:8)
On the words "ותקח המשרת - She took the pan", the gemara in Sanhedrin 21a says:
" and she should dress the food in my sight…And she took the pan and poured them out before him” (II Samuel 13:4–5, 9). Rav Yehuda says that Rav says: This means that Tamar prepared various kinds of fried [tiggun] food for Amnon."
And so writes Rabbi Simons:
"From all of this we see that the levivot are what we call today "sufganiyot". We will point out that among the foods that were with Yehudit were the ingredients to make levivot - Meaning, wheat and oil.
Due to the feeding of slices of milk (cheese) to Holofrins, the poskim wrote that it's traditional to eat cheese (or milk products) on Chanukah. We must therefore ask, if so, where is it mentioned to eat levivot on Chanukah?
In the halachic books and books of traditions (not including the books printed in our time!), the consumption of levivot in Chanukah isn't mentioned at all, but in songs and hymns it is mentioned. The first to mention the consumption of levivot on Chanukah was R' Kalonymus ben Kalonymus who lived around 700 years ago. In one of his songs (published in Sefer Even Habochen V'derech Hayashar to R' Kalonymus ben Kalonymus) he wrote:
"In the 9th month in Kislev:
A peaceful cry of the masses:
To Matity' ben Yochanan and not for shame:
And to the Son of Chashmonai:
And the important women collected:
Knowledgeable in the making of the food and preparation of the levivot:
Large wagons like the circumference of the pan:
And their sight [as] good as my wine and their order like the sight of the rainbow:
[They] bake the dough and all sorts of goods they make from the dough:
And on top of all they shall make flour of wheat:"
Hundreds of years later, in the beginning of the 17th century, the book Shtei Yadot by Menachem de Lonzano was published...in the fourth part of the song he writes: "Levivot with cheese on Chanukah, wafers in honey light for my candle." We see that according to Lunzano it was traditional to eat levivot with cheese on Chanukah, a famous dish at the time.
Also, there's a song for Shabbat Chanukah written by "Avraham" - some say Avraham ibn Ezra was the author and others not. The song begins with "Eat choice foods (משמנים) and fine flour cooked with oil" and brings all sorts of foods for the meal of Shabbat Chanukah. Some of the foods that appear in the song are foods known from other Shabbat songs, year-round, such as "swans" and "eat choice foods (משמנים)". But what is "fine flour cooked with oil"? Per Rashi's explanation of the meaning of the word "ותלבב", it's possible that the meaning of "fine flour cooked with oil" that is mentioned in the song is levivot (another option is that it is couscous, eaten on Chanukah by the Algerian Jews etc).
We are left therefore with question of why only the consumption of cheese on Chanukah is mentioned by the "Kolbo" and the Ra"n and the consumption of levivot isn't mentioned? As an answer, there's room to suggest that the reason that the "Kolbo" wrote "a dish of cheese" and not just "cheese" is that he was referring to the dish of "levivot filled with cheese".
In short, we see from here that like the custom of sufganiyot, the custom of eating levivot/latkes on Chanukah is also quite ancient, perhaps even from the time of Yehudit herself (that really depends on why the 1402 translation of Yehudit chose to translate the list of foods as including levivot (as discussed in the first section of that essay, different manuscripts listed different foods)), but the custom is certainly at least as old as Rabbi Kalonymus ben Kalonymus.
*For more info on the minhag of eating sufganiyot, see "Emek Hasufganim".