Record Level Access can control this. It uses the person's account or privilege set name and a "lock expression" to determine which records are accessible for that user:
To start see "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set this up.
And here's a second hint: Any find performed by the user or by a script will automatically omit records from the found set if access privileges don't permit the user to view the record. This can help keep the user from encountering records covered with a screen and the words <No Access>.
And a third hint: with FileMaker Advanced, you can set up a custom menu where a menu option such as Show All performs a script instead of the original action. This can then become a "show all allowed records" action instead of the original Show All Records..