You can find archived IPA files for older versions of YouTube on repositories dedicated to legacy software:
Disclaimer: Always comply with software licensing agreements and respect creators’ rights. This guide does not endorse piracy or unauthorized app distribution. youtube ipa for ios 1034 link
If your legacy device is jailbroken (the only way to effectively run modified IPAs), install tweaks from the cydia.akemi.ai repo. These tweaks patch the modern YouTube app to run on iOS 10, rather than trying to run an ancient version. This requires a jailbreak (e.g., Phoenix for iOS 9.3.5 or H3lix for iOS 10). You can find archived IPA files for older
Since the App Store won't allow a direct download for unsupported OS versions, you must use sideloading tools. you must use sideloading tools.