I didn't know that there were browsers that support JQuery!
JQuery is a JavaScript library, and all browsers support JavaScript. I have never looked in the JQuery library to see the kind of JavaScript code they use, but for now, all the JQuery instructions I have used in my websites work on all current browsers, even Edge.
But I have to confess, I only use JQuery for the past 2 years now, so maybe there are some routines in it that aren't supported by IE11 or Edge, but I haven't stumbled on them yet.
In fact, since IE11, I can now make websites without the need of extra CSS or whatever, to make it work crossbrowser. Since IE11 and HTML5, I started to make websites that only support IE9 and above. Anyone with an older browser, get the advice to switch to another brand of browser by me.
In the past, it really was troublesome how much extra code I needed to add to make it work in IE8- as it did in all other browsers. However, since IE9, and especially IE11 and Edge, they have a great support for HTML5/CSS3. And to be honest, I never have had trouble with JavaScript, and as an extension, with JQuery.
You're probably more advanced in your code than me, but at my level, which is rather advanced, as well; I never ran into a problem with the websites I created with all current browsers.
UPDATE:
I just found a nice page on the JQuery website:
Browser Support | jQuery
If any JQuery routine doesn't work, you need to contact them so they can fix it. I use JQuery 2, and they only give support for IE9+ for it. So... it's a good thing I also only give support for my websites for IE9 and up.