Running a MySQL query with an admin class
@Max already did a good job at describing how you could write better code. 

Here is what is wrong with your current approach:

The main problem is that your classes are tightly coupled. All the files you posted need to be aware that you are using PDO, which isn't good (it's hard to read and maintain).

Your admin class also doesn't make any sense. It doesn't contain code that is specifically concerned with anything related to admins, it just contains part of the database access code (but for some odd reason not all of it).

So what I would do now is:


keep all the PDO calls in one place. There really isn't a good reason to have prepare in one place, and execute and fetch in a completely different place. 
remove the generic runQuery method from admin, as it's not specific to admins.
move the admin select query into a method called getById inside the admin class.


Doing this, you basically arrive at the code @Max posted.

Misc


Class names should be upper-case.
Don't echo in classes, it makes them difficult to reuse. Just throw the exception upwards and deal with it later.
The way connect is written, you would use a new connection for each object. For example, if you not only had an admin class, but also a SomeData class, it would also call connect, creating a new connection. It's better to reuse the same connection across the request. So either pass the connection to the admin constructor, or to the getById method.
Try to be consistent with your names. Examples are admin_session vs admin_id, auth_admin vs admin, or conn vs db. These inconsistencies do decrease readability, as a reader has to think about them each time.
Either use camelCase or snake_case, don't mix them. 
Your spacing is off.