There are some dishes for which kanji was given later like Tempura, but similar to castella sponge cake, konpeito (confetti, candy), etc., kanji was not given for ojiya and it remained as its pronunciation, making people think it is a traditional Japanese dish.
テンプラなど、後に漢字が充てられたものもあるが、オジャは、カステラやコンペイ糖等のように、漢字が充てられず発音のままに名前が残った為、日本の伝統料理と思われているが、漢字が存在しない。