In the midst means in the middle of, surrounded by, among. Midst means the middle, it is a literary or archaic word which is not often seen unless used in the phrase in the midst. Midst comes into the English language in the mid-fifteenth century, from the Middle English word middes.
In the mist is an eggcorn. An eggcorn is a phrase that is misheard and misinterpreted from an existing phrase. In the mist, used correctly, means existing in a fog. Unless used to express this sentiment, in the mist is an incorrect usage.
Examples
Thane kids get green lessons in the midst of nature (The Times of India)
It is almost ironic that the pope has visited us while we are in the midst of one of the most divisive times in our history from a political perspective. (The Independent Mail)
America is in the midst of a bonafide lobster boom. (The Smithsonian Magazine)
In the midst of a lifetime of discrimination, the Bosnian native and war refugee saw his dreams smashed, but realized he had gained something much more important. (The Midland Daily News)
Prior to Saturday’s Bishop Heelan Classic, the 6-foot-1 Sergeant Bluff-Luton middle hitter was in the midst of her best volleyball season. (The Sioux City Journal)
That might seem like an oxymoron, but that is where the banking industry is headed, and locally Regions Bank is in the midst of a massive hi-tech overhaul. (The Memphis Business Journal)
Metric frontwoman Emily Haines may be in the midst of a European tour, but she’s still finding a way to rock the runway back at home in Toronto. (The Calgary Herald)
I’d stood there in the mist for a long time, wondering if it was going to be impossible to love, or to be loved, in this life. (The New York Times)