Host - Zabbix server
This host is in Host group Linux servers
This host has one active problem.

Create user test and grant him read permissions only to group Linux servers
As admin, edit Filter of Problems widget and specify that you want to see problems only from Zabbix servers Host groups.

Log in with test user, and you will see Active problem from Zabbix server host

User should see problems only from Zabbix servers host group