It is not possible to prohibit the editing of specific fields in a record that was created using the Duplicate Record icon. When a record is created using the Duplicate Record icon, the values of all of the fields into which values can be entered are copied, and the copied values become editable.

For your reference, below are the workarounds using the App Actions feature and access permissions.

• A workaround using the App Actions feature
  By specifying the same app (this app) for Target in the settings of the App Actions feature, you can create a button to transcribe (copy) a value of a specific field. This button can be used separately from the Duplicate Record button.
  Creating an Action to Duplicate a Record in the Same App
  
  

• A workaround using access permissions
  In the Permissions for Fields setting, specify a user for a target field and uncheck the Edit check box for the user. This prohibits the user from editing this field. When the user duplicates a record, the user cannot edit the field and the field is saved as a blank field.
  Configuring Permissions for Fields