Submit jsessionid with $.getJSON or $.ajax()

Submit jsessionid with $.getJSON or $.ajax()

Good Day

I'm making use of href URI e.g  <a href='<%=response.encodeURL("/navigate/home")%>'> which gets translated to something like /navigate/home;jsessionid=123456789, only when browser cookies are disabled. (The jsessionid is used for user httpsession tracking on the server side)

Question:
When using $.getJSON("/navigate/home") or $.ajax("/navigate/home") post/put/delete, how can I manage to append the jsessionid like the above example, only in case when browser cookies are disabled? Or can it be appended to the request header without being exposed on the URL path? If so, how?

PS: Does mobile devices/phones also make use of jsessionid's?

Thanks for the help
Nic