We use web based Visual Studio Team Foundation Server 2015 to manage test cases/suites/plans. If there is an way using TFS web based query to find Test Cases which belongs to specific Test Suite?
For now, there is no way to create ordinary TFS query via Web interface and not API call or custom coding to get list of Test Cases belongs to a specific Test Suite.
Since from TFS 2013 Update 3, test plans and test suites are regular work items, but there are of no practical use in work item queries, as there are no links between them and test cases.
With the links, you could create a query to list all test cases in a specified test plan. There has been a feature request in uservoice, you can also vote up for it to get more attention.
Support querying for "all test cases in a specifed test plan" a.k.a add work item links between test plans, test suites and test cases