To install YouTube on an iOS 10.3.4 device, you can use the official App Store "Purchased" method or sideload a compatible file using a computer. Method 1: App Store (Official & Easiest)
file (versions around 12.x or 13.x are typically the last to support iOS 10). Use Sideloadly : Download Sideloadly on your PC or Mac Connect Device download youtube ipa file for ios 10.3.4
Go to youtube.com in Safari. Then:
Which of those would you like?
Launch the YouTube app