Filtering custom post types and taxonomies by user

I’ve created a new custom post type and taxonomy to be used for a new user role. The new role is subscriber based but adds the capabilities of the custom post type and the new taxonomy to be able to add data.

I want to protect the records of other users added to the same post type. So far I have added one filter for parse_query that uses the author_id as a filter. But I still have links on the top of the pages to view all records regardless the author.

I cannot find a capability that disallows me to view foreign links. I simply want to authorize each user to be able to add records and not to be able to see other users’ records. I am not sure if that is applicable for the taxonomy – if I can select only taxonomy records created by this user? But I still need to be able to filter records by taxonomy as well.