I partitioned my harddrive as this for Ubuntu (ext4), a Windows 10 partition (NTFS) and a partition to keep data (NTFS). I wanted to change permissions of a SSH key on the data partition using chmod 400, but strangely the command has no effect. Also changing the permissions on the ext4 partition, then copying the file to the NTFS partition results in the key having permissions 755 again... the reason for all this is that SSH requires a key with permissions 400 to login to a remote shell.
What can I do here?
You set permissions for windows filesystems when MOUNTING.
But it will not fix your problem; you can not do what you want like that.
Permissions for a file or directory on a filesystem is a POSIX feature. NTFS is not POSIX. So you do not store ssh keys on a windows filesystem unless you can set the whole partition to 400.
Store the key in /home/$USER/.ssh/ like we all do ;-)