Good day developers!

A time ago I have made some new authorization that uses external API. API returns user data and ID number from the second system. According to all info, it's bad to add columns to the core database table, so I have made a new table for this that contains user class, school name, and external ID number. Bad thing is that, well I can store ID numbers in the moodle core system but the thing is that I need a class name that should be shown on all grading pages and also accepted in searching forms. I have already checked Moodle Additional user fields but will they show in the grading table next to users? 

Don't throw a link with a page that contains info about user profile fields, I have checked that already, problem is that I store these custom fields in another custom table. 

So what is the best practice to store additional data in a new table and let moodle find those fields?

Thanks.