Root [AT&T] Nandroid backups with locked bootloader

[By_design]

Most methods of nandroid backup utilize custom recovery modes like CWM or TWRP. I have a rooted Galaxy S4 I337 mf3 with no recovery mode to found, not even default recovery mode. What is the best way for me to do nandroid backups?

 

[argedion]

Most methods of nandroid backup utilize custom recovery modes like CWM or TWRP. I have a rooted Galaxy S4 I337 mf3 with no recovery mode to found, not even default recovery mode. What is the best way for me to do nandroid backups?

You need a custom recovery to do a nandroid backup. You state that the phone is rooted but is the bootloader unlocked? There is a difference in the two.