What should you do if your leopard gecko's tail is half way on and half way not on? Is it possible to prevent the tail from fully falling off? Can the tail reattach on its own by feeding her more and give her enough water? Shes only 3 months old and was born on 9-6-2017.
Leave her totally alone with no handling for 24 hours and see how she does. It's ok to feed her but if she eats crickets don't leave extras in the enclosure once she's done hunting. Most likely she'll drop the rest of it, unfortunately the likelihood of it healing itself is extremely low. I'm sorry :(
After the 24 hours, make sure to keep the wound, as well as her enclosure clean and dry, to protect against an infection and help healing. I would replace any substrate with paper towel and change it every day IF the change doesn't stress her out. If it does then do your best to keep the cage as clean as possible. Also you can put a very thin layer of polysporn on the wound every 2-3 days.
If the tail doesn't fall all the way off she may regrow a 2nd tail (it'll look like a forked tail). If she were mine, I would give it a couple days to see if it would fall all the way off and if it didn't I would take her to a reptile vet to safely amputate so she is able to regrow a new healthy tail. WARNING: Do not attempt to perform the amputation yourself - you need a vet to safely do it.
Send an update and pictures