Hi,
The printer drivers for this model from the HP support site appear to be for very old Mac operating system versions.
Any information about the macOS version on the MacBook Air? What kind of printer driver are you using?
If necessary, you could perhaps try the HP 5.1.1 Printer Software Update package download from Apple instead (despite the system requirements limitation). Look upon this as an experiment. This may or may not work with your printer. Look for something like the HP Deskjet 3050 J610 series version 2.3.2 driver listed in the referenced article Printer and scanner drivers for Mac - Apple Support.
You may have to reset the printing system (link below) between tests.
If there is a problem with USB, you may want to test a wireless connection via a Wi-Fi router instead.
As always, make sure that you have backup copies of all important files before testing anything. Software conflicts can never be ruled out.
Add a printer to your printer list so you can use it on Mac – Apple Support (UK)
Reset the printing system on your Mac to solve a problem – Apple Support (UK)