You can download songs from the YouTube Music app to an SD card. You can also download to your phone's internal memory using the Download button 
How to download songs to an SD card with YouTube Music
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Download music to your phone's SD card
To make sure that the songs you've downloaded are stored on an SD card, install an SD card on your phone.
Save to SD card by default
- At the top of your screen, tap your profile picture.
- Tap Settings.
- Select Downloads.
- Switch on Use SD card (Save music to the SD card).
If you don't turn on SD card use, your music will be saved to your phone's internal memory. Make sure that there's enough space available on the SD card to save your music.
Download videos to SD card
If your device loses connection while downloading, the download will resume when you reconnect.
- Go to the song that you'd like to save to your SD card.
- Tap the Download button
below the video or select Download from a video's Menu
. The Download button will appear blue
below the video once it has been downloaded.
. The Download button will appear blue 
below the video once it has been downloaded.If your device loses connection while downloading music, the progress will resume when you reconnect.
SD Card FAQ
How do I move downloaded music from my phone's internal memory to my SD card?
It is not possible to directly move songs from one location to another. To move a downloaded song from your phone's internal memory to your SD card.
- Delete the song from internal storage.
- Change the storage location to SD.
- Download the song again.
How do I move downloaded music from my SD card to my phone's internal memory?
It is not possible to directly move songs from one location to another. To move a downloaded song from your SD card to your phone's internal memory.
- Delete the song from your SD card.
- Change the storage location to your phone's internal memory.
- Download the song again.