Try connecting the external hard-drive to a different computer. If it still fails, and it is still under warranty, then exercise the warranty to get it replaced.
If the warranty has expired, open the case, and remove the disk-drive, disconnecting it from the USB-to-disk-drive adapter.
Connect the disk-drive as a "slave" disk-drive in some desktop computer, to see if the disk is recognized. If it is, then the USB-to-disk-drive adapter has failed, and you could go to any computer-store to buy a new external case and adapter, and mount your disk-drive inside the new case, and work with your files.
If the disk-drive is not recognized, check the warranty on the disk-drive itself.
Answers & Comments
Try connecting the external hard-drive to a different computer. If it still fails, and it is still under warranty, then exercise the warranty to get it replaced.
If the warranty has expired, open the case, and remove the disk-drive, disconnecting it from the USB-to-disk-drive adapter.
Connect the disk-drive as a "slave" disk-drive in some desktop computer, to see if the disk is recognized.
If it is, then the USB-to-disk-drive adapter has failed, and you could go to any computer-store to buy a new external case and adapter, and mount your disk-drive inside the new case, and work with your files.
If the disk-drive is not recognized, check the warranty on the disk-drive itself.