Updating a iPad mini 3 with higher software then the 9.3.5

The original (1st Generation) iPad mini cannot be updated beyond iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular).

Apple formally ended update support for these devices in September 2016. None of these models can be updated to iOS 10 or later versions, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS.

By contrast, an ipad mini3 can be updated to iOS 12.4.5/6.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12 - and have withdrawn older versions of their Apps from the Apple App Store. Difficulties finding compatible Apps obviously limits ongoing utility and usefulness of old devices.

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. Even the basic current iPad model supports current iPadOS 13.x - and has hardware specifications that will vastly outperform your old iPad

I hope this information is helpful - if only in clearly stating your current options.

Yes.

Lets start with what you actually have. What is the exact model number of your iPad - as displayed in Settings?

Settings > General > About