can my old IPad mini be updated on the OS beyond 9.3.5?

No.

Your iPad model is too old, now.

Sorry.

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a new iPad model OR a much “newer” , used iPad model capable of running the latest iPadOS versions.

There are plenty of newer, older iPad models that can run the latest, current versions of iPadOS.

Sorry & Best of Luck to You!

Sorry, no, not possible.

iPad2, iPad3 or original iPad mini cannot be updated beyond iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular).

Apple 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. The 32-bit architecture upon which they are designed is obsolete.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store, now limiting utility and usefulness of older devices.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. Of current models, even the entry-level iPad8 supports current iPadOS 14 - and has hardware specifications and capabilities that will vastly outperform your old iPad.

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

If you have the 1st generation iPad mini, it cannot update past iOS 9.3.5 or iOS 9.3.6 for cellular models.

The iPad lacks the required RAM.

If you want to update further, you need a newer iPad model.

Sorry, no. Your iPad is too old, and the max it can go is 9.3.5/9.3.6. To get past the max, you have to get a new iPad, or a more “recent” model.