Can I recover files removed from backup

I kept getting messages that I didn't have enough space for backup and needed to pay for more.

I was backup to my external hard drive. I tried to create backup on Norton eliminating music files because I have them on my external hard drive. This was about a month ago. I have been looking on my external drive for 2 days and can't find any of my music files.

I assume I somehow lost my files trying to save space on Norton Cloud.

 

I tried to create backup on Norton eliminating music files because I have them on my external hard drive.

Do I understand that you created a new Backup Set without music files? 
And you saved that new Backup Set to Cloud Backup. 
And then you could not find your music files previously saved to your local external drive. 

?
 

To confirm. You had both your music files and your Norton Backup file sets stored on the same external drive?

If so, and you deleted your music files, intentionally or not, and you have done backups since that deletion of the music files, then it is highly unlikely that you would be able to recover them. As the backups were stored to the drive, it is quite likely that they over wrote the same portions of the hard drive, removing any chance of recovery.

You would have to look for some reputable file recovery software to even try to recover any deleted files.