What's the exact error message you see?
If that's indeed OneDrive folder(not just named OneDrive) you would need to disable VSS for that plan to be able to back those files up.
In addition to that you would need to disable "file on demand" functionality.
All of this is related to the recent MS updates, they decided to disable VSS access to OneDrive folder.

Hi, Matt.
With OneDrive Files On Demand enabled and files set to "Free up space" (i.e., file is in the cloud with a local stub), we will receive backup errors for these files and also to their counterparts under VolumeShadowCopy - Error = "Access to the cloud file is denied."

The property details for a file physically on the computer vs stubbed (sure you already know and understand this more than us...):

File on the device:
Attributes: AL
Availability status: Available on this device

Stubbed files ("Files On Demand"):
Attributes: ALOM
Availability status: Available when online

Could we have an additional option under Advanced Filter in the plan Wizard something like:
Do not backup files only available when online ("OneDrive Files On Demand", "Dropbox Online Only")

It's interesting that I don't get errors for files that are online only for my personal DropBox or corporate DropBox or for my corporate OneDrive for Business.

With "Use Block Level Backup" and "Use Fast NTFS Scan" enabled (both forcing VSS) my backup job runs about 3-5 hours. I disabled both of those settings (so VSS would not be used as suggested) and I still get the backup errors on the OneDrive stubbed files (and 3+ hours for the job). Last backup job (typical): 40 files uploaded (146MB), 147606 files scanned, 135GB scanned, 14126 files failed to backup (all OneDrive). Running 5.9.4.245.

I understand Microsoft is changing things up on you, but hopefully you can work out a solution soon.
Thanks.

Until Microsoft does something about the situation and how files like that are handled we can't really do much on our side.
Creating a separate plan with VSS disabled along with "file on demand" option on OD side for such data is the only workaround I can suggest.
I already created a feature request regarding this problem, some improvements should be implemented in version 6.2.

Something really needs to be done about this. If you can't back it up, at a minimum MSP360 should be adding an option to suppress backing up these files so that it doesn't cause an error. We really need to be able to specify backing up an entire profile without having to resort to examining the profile to not back up the cloud directories.

Things actually progressed since my last post. The software will be able to handle such files starting from version 6.3 which will be released this Spring.

Matt thanks for the update, and that is really good news. In what way will the new release handle these files? By skipping them, or does it back up the stub? I would prefer to back up the stub if it is possible to do that.

According to the latest info there will be an option to either skip the files or download them from OneDrive and transfer to your backup destination.

Great, I look forward to it.