Permits are only available for systems - there are no region or planet permits at this time[3].
You can check which permits you have in the right panel of your ship - look at the Status tab and move down - one of the lower sections lists permits you have.
OTHER SYSTEM PERMITS
Most other systems will let you earn their permit by becoming allied with a permit vending faction (exceptions are noted with the system description). The controlling faction is not always the permit vending faction. Once you reach the required level of reputation you can take a simple mission on the mission boards for that faction (only ship missions, not on-foot in Odyssey).
You can rep up (to become allied) at any place the faction is present, but only systems within 20 light years [1] of the permit faction's home system [2] will provide the mission to get the permit. The eddb listing for a faction gives the distance from the home system next to each system. Permit missions will not show while the faction is in a conflict (War/Civil War).
Thanks to:
This post based largely on data from CMDR Swift Arrow's Updated Permit List post
https://forums.frontier.co.uk/threads/updated-permit-list.122593/ which doesn't seem to be updated any more