It is not possible to set server side property like from javascript alone. You need to do postback or send ajax request to update the server side variable.
Server side code generates the html / javascript and send to the client. The value of property is set in html like a string literal and sent to client. Server side (asp.net) variable does not exists on client (javascript).
You can assign javascript value to some hidden field and get that hidden field on server to assign value to property if you want to do it through postback. If you want to do it with jQuery ajax you can pass pass the values in data in jQuery ajax() function. If you only need to update some value on server you better choose ajax to prevent whole page refresh.