Restricting the trigger to fire only selectively

Hello everyone

We are looking for advise on one issue that we are currently facing on our 11.2.0.4 Database

We have an "AFTER INSERT" trigger on a table ABC that INSERTS records in a table XYZ when fired

Would it be possible for this trigger to FIRE only IF the user or the machine or process matches a given criteria?

Like for example, if the owner of the process or module that is inserting data in the table ABC is USER_ABC or module is MSACESS.EXE , only then FIRE the trigger

OR

Similarly, if the owner of the process or session that INSERTS the records in table ABC is USER_XYZ then do not fire the trigger. If it is any other user, then fire it