All the 70-300mm lenses on the market are f/5.6 at the long end, so they will generally not autofocus when used with a teleconverter. Some third-party teleconverters play tricks to disguise thair presence, fooling the camera into thinking the lens is still f/5.6 instead of f/8, and then the camera will try to autofocus; but at f/8 it will struggle.
Generally speaking only telephoto primes and pro-spec telephoto zooms can accept a teleconverter. Many other lenses can be phyically damaged if you try to fit a teleconverter. I'm not aware of any 70-300mm lens which is recommended for teleconverter use. Certainly you couldn't use a Canon teleconverter; you might be able to use a third-party one if it doesn't have a protruding front element, but be careful.
So to summarise:
(1) 70-300mm lenses are not designed for use with teleconverters and you'll have to hunt around to find one which can fit without damaging the lens.
(2) If you can find one which will fit, it probably won't autofocus.
(3) Image quality will take a big hit.
Still want to do it?