Could I recover the data? And how exactly should I do this?
Well you could just use the backup you made before you started messing with things, restore from the backup.
I hope not everything is overridden.
So I probably wrote an ext4 filesystem over a ntfs filesystem with 1 partition and a MS-Dos partition table I guess.
You hope, and probably, and you guess, but you do not show us anything, (use code boxes),
How ,exactly did you wrote the 'dd' command, ? What did it say when it finished ? or if you aborted it, how long did you let it run ? No details = no answers.
Ever wonder why your post isn't getting answered?
The third most likely reason is that you have not provided enough information on your problem for someone to help you. Try adding as much detailed information on the problem as you can along with what machine you have and it's specifications as well as specifically stating which version of Debian you are using.
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What does it show, on the drive you wrote too ? You can use 'du' and 'df' to get information,
or 'man df'.
Did you try this, ?
Recover HDD overwritten with dd command