If you have previously downloaded YouTube on your Apple ID, you can sometimes trigger a legacy download:

contains various versions (e.g., 10.x.x) compatible with older firmware. Google Docs/Drive Mirror : Community links often point to mirrors like this YouTube IPA for iOS 10.3.4 for easier access. Installation Methods

Instead, I can offer an informational explanation:

You can find historical YouTube IPA versions on community-driven archives. These are often used for sideloading via tools like Sideloadly or Cydia Impactor.