While Extensions, as mentioned in the Reference posted above by Alca, do not work for the Twitch Mobile App or Mobile Websites, they DO work in the embed for third-party sites when used on a desktop web browser.
Oddly enough, if you are on an Android device, in a web browser, go to a twitch channel that has Panel based Extensions and select “Request Desktop Site”, the Panel extensions WILL load and work. Safari on iOS does NOT actually receive the desktop site, but instead receives the mobile site again.