my phone is locked how can I back it up

What does “locked” mean exactly?

• Passcode locked? If you forgot your iPhone passcode - Apple Support
• Activation locked? How to remove Activation Lock - Apple Support
• Carrier locked? How to unlock your iPhone for use with a different carrier - Apple Support
• Something else?

LTOL9 wrote:

how can I back it up

Backups must occur before catastrophes. After a catastrophe it’s too late.

by locked, you mean disabled or showing the restore screen?

At this point it's too late to try and recover anything. You'll have to rely on your most recent backup

If you forgot your iPhone passcode - Apple Support

If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support

You will have to get that iPhone “unlocked” from AT&T first. Contact AT&T.

Axel F.