If you just want to export/import the Test Cases with the basic information, then you can export test cases from VSTS to MS excel, then edit and import to on-premise TFS, reference this thread: How to Export and Import Test Cases from Visual Studio Team Services into MS Excel
But it's difficult to migrate/duplicate Test Cases separately between VSTS and TFS with parameters and attachments. See Bulk Migrate Work Item Comments, Links and Attachments
Test Cases
Test plans/suites/cases turned out to be particularly
difficult to migrate. We couldn’t find any tooling that would be able
to do this for us. It’s possible to manage tests using the TFS SDK
on-premise, and there is a restful API for VSTS, so a custom solution
could be produced where time is permitting.
Unfortunately, Excel was out of the question, as test plans and suites
cannot be queried as usual and test cases when published were not
possible to be linked to a test suite or plan.
Source Here
You can also reference below similar threads: