Unless you can provide further context here the only situation that comes to mind would be something like this:
"I saw it in a video on Youtube" implies something was part of the sequence of events of a video e.g. the content of the video was a man jumping.
"See Transformers on video now" goes back to the days before DVD where we had video cassettes, and to say a film was on video meant you could rent/buy the film stored on a video casette.
I can't immediately think of a context for "on a video" it is said a lot in conversation instead of "in a video" like my example above, but strictly speaking it's wrong in that situation.