You know, that’s an interesting question. It looks like the answer is probably 1, but it might be 2.
It’s not entirely clear to me, but it looks like Ulysses S. Grant may have been arrested in 1872, while he was still in office. For speeding. On horseback. The practice of taking mugshots on arrest began in the 1850s, but the officer apparently did not take the president into the station, so while I bet no mugshot was taken, I haven’t been able to completely rule it out either.
Then after traveling for some time, Grant did attempt to run for office again, but failed to obtain the number of required number of votes for nomination, and a compromise candidate was chosen (Garfield, who got assassinated), but he did technically run.
Apologies if I’ve used the wrong terms or gotten some bits wrong. My knowledge of the US political system is vague at best, I’m nowhere near you guys, I’m just having a terribly slow day and work and wondered if this particular situation actually had happened before. Then I found an unexpected rabbit hole of weird historical half-truths.