What is the shortest recorded prison or jail sentence in US history?
Likely an extremely hard or impossible question to answer, and may very well be one that may, barely anyone would go to appeals for a sub-1 day sentence, and it searching superior court decisions is far from well-digitized, and there are over 3,000 counties in the U.S.. Since they generally have no binding effect on future cases there is no incentive in digitizing older cases at all. I would not be surprised if during the history of the U.S., certain courts would have lost their past records for example in fires, earthquakes or other acts of God, including of such cases that no one remembered at the time, and no other record existed of any more.
If you're lucky, some historian may have somehow answered this question, and is somewhere as a trivia. Also, I have never heard a sentence to be expressed in hours, minutes or seconds, so likely the answer will be a single day which plausibly could have happened where other remedies were not appropriate (defendant not having money and incapacitated from being able to do community service or engage in labor or service in servitude per a sentencing).
UPDATED — There is record, in fact, of a 1906 case where a judge sentenced a man for 1 minute in jail for "being drunk and disorderly" "what was probably the lightest sentence ever given a prisoner, that of one minute in the county jail[;]" (The One Minute Jail Sentence) but of course, even less than a 150 years in the existence of the Union, they could not assert that with certainty.