Add user defined field to test case to Quality Center

Add Custom Field
You need admin right to do this
Tools > Customize
Project Entities > Test > User Fields
Select first ZZTC_Customize_AlfaNum_xx field

Make it visible
Tools > Customize
Groups
Select the group
View
Select Tab Test Cases
Select "Test Cases Data-Hiding Filter"
Select Tab Visible Fields
Mark your new field
Click OK
Close and Save

Now it should be visible