Can anybody help me with my Seagate Expansion drive?

Pull the hard disk out of its case and put it in a new case.

Or try to reseat the cable receptacle so the cable makes a connection. 

you need to remove it from its enclosure, and connect it to a desktop computer internally, not through USB.

The only reasonable answer you have had is from Rayal although he has had a thumbs down.

Remove the drive from its case and purchase a new case. There are plenty available for sale 

Depends on exactly which drive it is.  Most expansion drive until the last year or two are regular internal hard drives inside of an enclosure.  They are attached to an adaptor that lets them connect to a USB cable.

Usually you can (carefully) open the case and extract the hard drive.  You can then attach it to your computer as an internal drive.  Or if you have a laptop (which no space for an internal drive) you can buy a cable that attaches the drive to your laptop.

The enclosure interface is damaged, contact maker for a replacement. If just loose, maybe a spot of glue might tighten it down.  I would not advise trying to solder anything--heat might make it worse.

Cannot pull the disks out of a sealed hard disk chassis without loss of most everything.  Must be done in a Class 100 clean room, and the read-write heads must be re-aligned to the data tracks when put into a new case.

Contact a data recovery company.  Be prepared to pay a lot.  I have seen one advertised that doesn't charge if they believe no helping can be done.

That is all that can be suggested with no model number or picture or first person inspection.