Ok.. unless you created a virtual disk.. you did not actually partition a real disk.. you partitioned Time Machine's sparsebundle.. some web sites even advise this is a valid way to work with a TC.
It isn't.
A sparsebundle will be deleted by time machine when it is detected as corrupt.. an event that happens regularly. All your files will then be deleted.
What is more you have made the sparsebundle just that much more fragile as it can now be taken over as files are written to and from your new "partition".
My strong recommendation is you wipe the TC and start again. Use quick erase from the disk tab in Airport utility. Then do a fresh clean Time Machine backup. Do not ever touch that sparsebundle again unless you are restoring from it.. it belong wholly and solely to Time Machine.
You can create virtual disks with Disk Utility as Bob noted.. these are created under the Data main share.. fine and dandy.. You can even create a virtual disk from Windows that will be treated as NTFS.
See
Possible to create a windows VHD file on the TC.. format it GUID/NTFS and mount it to the windows computer.. Windows believes it is NTFS formatted.
From Finder it looks like a single large file just like sparsebundle.
https://discussions.apple.com/thread/7634417?answerId=30518554022#30518554022
But what is usable in windows is not usable in the Mac and visa versa. If you want a shared directory for files just create a folder under Data and yes, it can have permissions issues to another Mac but Windows pretty much ignores permissions.
You cannot create virtual disks for sharing between computers.. and never ever use FAT with anything in front or behind is still a weak file system.. Windows can write to HFS+ (Mac OS format) just fine as long as it is network drive and it is using SMB protocol.