I just want to know a way out to preview quicktime(.mov) on modern browsers (Windows specifically!).
I'm very well aware that modern browsers doesn't supports quicktime containers out of the box and old solutions like embed and object tags doesn't work anymore due to no related plugins.
I've been crawling through a lot of resources and all of those are pretty outdated and doesn't work for modern browsers. Let me know if I need to mention those!
If you mean to preview the video when you hover over it, this is not part of the standard HTML5 video tag functionality.
It is usually implemented in JavaScript, either in a 3rd party player or sometimes inline with the HTML5 - e.g. by adding something like this in the video tag:
Quicktime support is a separate issue and as you say support is not strong across browsers - the best place for the current view is usually the Mozilla info: