You can keep the video running even after locking your iPhone screen. Note that you simply cannot do picture-in-picture from the YouTube app. To focus on YouTube videos within the background, you want to open the video within Safari. ... this iOS feature is not a complete YouTube premium replacement. Follow steps.

 iPhone Home Page


Click on safari 


Open Safari and go to 'YouTube.com

Click the share option


And select Request Desktop site


Now YouTube is open on  desktop interface


Now YouTube will open on desktop

Now play song and 

Go to home page 

Now play song and Enjoy


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