Apple - Shortcut to insert / paste email address?
Built in to the operating system is text replacements, so if you open Settings -> General -> Keyboard -> Text Replacement you can add your own text replacement shortcuts. For example, you might add "e@" and have it expand to your full email address, such as "[email protected]". It will automatically expand when tabbing away from a field or hitting the space key on your keyboard.
It seems the Clips app provides what you're looking for. It's basically a clipboard manager, which comes with a custom keyboard extension that lets you paste copied texts into text fields. It's a free app available in the App Store.