You can't do that on a save and continue button.

If you want to add JS to a button you need to choose the JavaScript option, name it Save and Continue , then add in your code to do what you need to do, which would be save the form in current state plus whatever else you are trying to do with code.

Thanks Ben for suggestion. I am not sure, with  Javascript type of button, of we can skip form control validations.

But i have resolved with below way:

I have added few lines of code in Nintex form custom JavaScript settings, and my job is done

$("input.myDraftBtnClass").click(function(){
//do something
});

myDraftBtnClass - is class applied to my "Save and Continue" type of button.