By Quick Saves, I mean those that are immediately deleted when you load them : they let you save your progress so you can resume later, but prevent save-scumming, unlike regular saves. They're seen in most RPGs, where dying sends you back to your last proper savepoint, serving as a means to stop playing at any point, should something come up, without allowing to save anywhere, which would severely undermine the tension those games need to be fun in my opinion, so it's a pretty big problem.
While normal saving is as easy to perform as choosing the corresponding system action, I can't seem to find anything about making Quick Saves nor do I have any real idea how to do it.
So, When I think of a "Quick Save" feature, I think of being able to quickly save a game, (by pressing a button or icon) without having to go into menus or dialogs, or save points. I'm not sure I understand the need to delete the save. I would make the quick save feature simply save to the same file/location each time evoked, overwriting the previous quicksave.
BUT... If you think there is a need to delete the save, after used, then you're looking at creating some custom metadata for the save and possibly even some custom scripting. The closest thing I could find to what you're looking for is in the How to make savegames tutorial:
Tracking which slots are used
The system save/load actions don't tell you which slots have been saved to. The best way to track this is to store some extra meta-data yourself in the WebStorage object. For example, whenever you save to a slot, also write a WebStorage key that indicates the slot has been saved to. You could add some other metadata like the player name or even a small screenshot of the game as a data URI. Then you can tell which slots are in use from the WebStorage data you've saved. You can perform other operations like resetting or clearing save game data just by adjusting these meta-data keys, such as removing them to make it look like the slot is empty again.
Haven't tried to edit WebStorage objects myself, or try anything close to what is mentioned here but, this may be the breadcrumb trail you're looking for. Only other thing I can think of is, when a player dies, present them with possible saves to load from, and simply do not present the quick save as an option. Hope this helps. Let us know if you figure it out. Good Luck!