Read permissions to data stored in schemas depends on the type of data the schema is used:

• Page Data is metadata associated with the specific page and hence shares the page's access rules. Eg. You can see or edit the data only if you can see or edit the page. (Also note the setting visibility → ineditor for data types in the schema editor)
• The same restrictions apply to serial data.
• Global data is basically always public, but editing can be limited to groups and users in the schema editor, see configuration to set permissions for allowed editors.
• To allow a user to use a schema you must also add that user to the “allowed editors” at the bottom of the schema editor.