from my point of view I think there’s not many hope. Because you formated your ntfs-partition with ext-file system. But perhaps I’m wrong (what I hope for you).
At all I would recommend to install the package ‘testdisk’ from the repos. This package includes the applications ‘testdisk’ and ‘photorec’, which are good software to recover deleted files.
I don’t give you much hope. ext4 set sectors to zero thus overwrite it on creation. Partially you could recover it, but must of it would be just junk. So a simple “undelete” will not work here.
Noting that the drive is NTFS, your best hope would be to connect the disk to a Windows environment, and use native tools to recover files. That said, it’s unlikely the entire filesystem can be recovered; but at least there’s a fair chance of revovering the files you wanted to keep.
If you do not have a Windows installation, this could also be achieved via a VirtualBox Windows Installation; albeit likely to take much longer.
In a Windows environment Recuva is a capable free recovery tool. Cheers.
Update:- I missed the most important part of your question; that you have formatted as ext4 – therefore, please ignore the above content. I’m in agreement with Megavolt; recovery is unlikely.
However there are Linux Recovery Tools available for the purpose.