My iPad can't download ios 15.0.1 stalls on verification

First it may be worthwhile to understand that the iPadOS 15.0.1 update addresses two very specific issues - namely (1) incorrect reporting of free space and (2) unlocking your iPad using an Apple Watch. If you currently have iPadOS 15.0 installed and are not impacted by either of these issues, then the iPadOS 15.0.1 update offers no benefit.

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

If you continue to experience difficulties with direct update from iPad Settings, you may have more success if you perform the update using a PC or Mac computer. To do so you will need access to either a PC (with iTunes installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

If you are still unable to install the update, the technicians at the Genius Bar of your local Apple store or Apple Authorised Service Provider (AASP) will be able to assist.