Minute as a time unit for scheduled reminders
It's a legitimate question although even if you could do it per minute, you'd then have to have cron run every minute, which is technically possible but might be a bit excessive.
If you're talking about reminders for activity assignees, an alternative might be to turn on the setting at Administer - Customize - Display Prefs - Include ICal Invite to Activity Assignees. Then they can put it in their calendar and they can set it to remind them as desired.