My Ipad won't download IOS versions after 10.3.4

Hello. Your 4th generation iPad is an older device and cannot run any versions of iOS later than 10.3.4. If you would like to upgrade to a newer version of iPadOS, such as iPadOS 15, you will need to upgrade to a newer iPad. A list of supported models for iPadOS 15 is available here.

Hello ~That is the highest iOS possible for that device. If you need/want to use a higher version of iOS you will need a newer device. Take a look here:

Buy iPad | Apple Official Site

Also if you want to purchase a second hand device please take the time to read this information:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Also:

The All Too Common SAD Reality of Buying a Used iPad/iPhone

~Katana-San~

Further update of your iPad4 is not not possible.

Update support for iPad4 ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions. The 32-bit platform upon which the iPad4 is based is obsolete.

Many App Developers have also dropped support for 32-bit devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited. Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Of current models, even the entry-level iPad9 supports current iPadOS 15 - and has hardware specifications and capabilities that vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly stating the fundamental limitations of your iPad4 and your available options.

iPad (4th-gen) doesn't support a higher version than 10.3.4. To update to iOS 11 or later, you will need a different device.