How did the word "ketchup" come into the English language? Apparently, there are three primary theories regarding its introduction into the English language from Chinese. 
The former is from the Cantonese "keh jap" or equivalently 茄汁, literally translating as tomato juice. 
The latter attributes its origin to two words in the Hokkien dialect in South Fujian province. The theory is that ketchup deviates from the word 'koê chiap' or equivalently 'kê chiap'. This, on the other hand, translates as fish sauce, or for in a more specific context, brine of pickled fish or shellfish.
Intriguingly, the Mandarin translation of ketchup today is 
番茄酱. It differs from the original 茄汁 or 鮭汁, of potential interest to linguists.

Would anyone have any information as to where exactly the word "ketchup" originated from in China? Or possibly shed some light on the matter?
As a ketchup lover, and a fan of Lea &amp; Perrins Worcester Sauce, I can see the Chinese, fishy-brine, vinegar-based connection.

Have a look here. Especially 3、

One of these words may be the Daddy of the word ketchup: 茄汁”、“鮭汁”、“醢汁