醤玉子 is not a word people know, and thatwhich means no one knows its correct meaning or reading. If this is not your own made-up word, then you probably misread something, as droooze pointed out. Unsurprisingly, you cannot get anything useful if you put an entirely new word/phrase to Google or a dictionary site.
Also note that 醤 and 醤油 mean two very difficult things, just as "soy" and "soy sauce" are different in English. 醤 by itself means something like "(spicy/salty) fermented paste", and it appears in the names of various Asian seasoning materials. Generally speaking, 醤 is read "ジャン" if it's part of the name of foreign paste (e.g., 豆板醤 = トウバンジャン, 苦椒醬 = コチュジャン).
If I somehow had to assume 醤玉子 is a correct word and had to guess its meaning, I would probably think it's a rare non-Japanese dish which has nothing to do with 醤油. This is because, as a native speaker, I know Japanese better than any other languages and I know 醤玉子 is not a traditional Japanese dish. As for the reading, it's difficult to guess, but しょうたまご, ひしおたまご and じゃんたまご seem equally possible to me.