I have an app which has a feature A which should run in background every minute.
That will not happen on hundreds of millions of Android devices, those running Android 6.0 and higher, due to Doze mode (and, possibly, app standby, depending on the rest of your app).
But AlarmManager seems to be a good candidate for the problem because when permitted they exist even after system reboot
No, they do not. You need to reschedule all alarms scheduled with AlarmManager after a reboot.
the Alarm Manager is intended to be used for tasks that have to be run at a specific time
AlarmManager supports repeating options.
This is more for tasks like downloading in the background as I have read and not intended for doing something I have explained.
A Service will be essential for whatever solution you wind up using.
JobScheduler seems not to be for a task that has to be done in permanently, but for tasks that fulfill a specific constraint like idle, or no network
JobScheduler, as with AlarmManager, supports repeating jobs.
So which of these (or other ones if they exist) do you recommend to use for the task I explained in the first part
Use none of them, as you cannot run things every minute on Android 6.0+ once the device goes into Doze mode, which will be within an hour of the screen turning off. Instead, either redesign the app to only need background work a few times per day, or do not bother writing the app.