can i use disk partition for time machine?

It is preferred to create a separate physical partition/container for Time Machine. There have been numerous reports of issues when Time Machine is a volume within a container. Some that show up quickly and others that show up when people have most needed it. And sometimes it works fine.

In reality, the most reliable method is to have a dedicated disk drive for Time Machine.

Yes. Is your external volume set up in an APFS Container? If so, add another volume for Time Machine. The available space is shared between all the APFS volumes in the Container. It is also possible to assign a disk quota to the Time Machine volume. As far as I'm aware, assigning a disk quota can only be done from Terminal.

- Pie Lover

There are risks when using the same drive partitioned on one side for Time Machine Backup and the other partition for Archiving data.

External Drive are known to fail and will at sometime. With this setup as above - if or when the drive fails - Everything is lost and in a drive failure - all is lost without a way to recover important data.

Do you have a Rescue Plan In-Place. This comprises having 3 Backups using 2 methods and 1 Off Site incase of Theft, Loss or Natural Disasters. A Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS. 

For addition purposes - two Tested Bootable Clones each to separate external drives. This is insurance incase the upgrades goes sideways. At least one Tested Clone and / or Time Machine Backup should be Off - Site

I don't doubt what you're saying. In my case, I have successfully been using Time Machine in this way since Big Sur allowed APFS Time Machine volumes.

I should probably mention that I actually use 2 Time Machine volumes. One is used in the normal way. The second is not connected to the Mac except for a daily snapshot each morning. My hope is that this scheme will offer some protection in the case of multiple failures.

- Pie Lover

BlueberryLover wrote:

I should probably mention that I actually use 2 Time Machine volumes. One is used in the normal way. The second is not connected to the Mac except for a daily snapshot each morning. My hope is that this scheme will offer some protection in the case of multiple failures.

... except if the whole backup drive fails. In case you aren't doing so already, it would be best to include additional backup methods in your overall backup strategy ... like, including disk cloning with something like Carbon Copy Cloner.

The second Time Machine volume is actually on a separate external SSD. I used this same SSD for backing up (original) photos and storing (barebones) older macOS versions (Catalina and Big Sur).

I've been thinking about purchasing another larger SSD. In that case, I would probably dedicate an entire SSD for Time Machine backups.

- Pie Lover