How can I listen to Youtube with my screen off without a Youtube Premium subscription
You can download: YouTube Vanced. I am using this app myself and it works like a charm. You can also turn off the screen and still hear the music playing.
There is a solution, if you want to listen YouTube song even when your android phone is locked. To do that you have to use chrome browser in android phone. Open YouTube in chrome browser and request as Desktop Site and search for the song which you want to listen then minimise it. The song will be paused then, from the notification you can tap on the play(▶). By doing this you will be able to listen YouTube videos in your phone even if it is locked. I hope this will help you.
OGYoutube can play with screen off.
But oddly it cannot play while minimized, which means you can only listen when not using the phone with other apps.