The name of this popular snack literally means "ghosts in scalding oil" and there are at least two accounts of how it originated.

Legend 1:
It refers to the legend of two lovers who were sentenced to be boiled in oil. As they were submerged they clung together, which is why 油炸鬼 are made as two conjoined breadsticks.

Legend 2:
油炸鬼 was orginally 油炸檜 , named after the prime minister and national traitor Qin Hui (秦檜) during the last days of the Northern Song dynasty.
According to tradition, after news that General Yue Fei (岳飛) was murdered by Qin and his wife got out, the people of Hangzhou (杭州) became extremely angry, hating them to the point of wishing to deep fry and eat them.
At that time, the chef at a shop that specialised in deep fried food took some dough which he kneaded into the shape of a man and a woman. He stuck it to together, deep fried it in a wok and shouted: "Come eat my new treat, 油炸檜! Everybody come quickly to enjoy it!"
Since so many people vied to buy it to eat, everyone in Hangzhou ate the new dish. This treat then quickly spread throughout the whole of China.
Over the years, 檜 ('hui') mutated into 鬼 ('gui'). 秦檜 probably did not die in boiling oil, but his wife was as much a national traitor as him. It was possible that the two bread sticks were meant to refer to 秦檜 and his wife. However, even if there was any love between 秦檜 and his wife at all, it was most likely not remembered and definitely not celebrated.