How can I reset the restrictions code on my son’s iPhone 4?

If you’re referring to screen time, you’ll have to reset the iPhone and not restore the backups; basically, to start over.

There’s no reset as far back as the iOS available on an iPhone 4, and restoring the iPhone backup will restore the screen time password. iPhone 6s and newer have a screen time passcode reset, on more recent iOS versions.

This is the newer procedure: If you forgot your Screen Time passcode - Apple Support

Parental Controls was subsumed into Screen Time somewhere between this iPhone 4 and current. At iOS 12, IIRC.

The passcode reset involves resetting the device, and not restoring the backup.

https://discussions.apple.com/thread/8312497?answerId=33133375022#33133375022