TGS-T350 SSD Not Visible To Fedora System

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I suggest running dmesg from console just after pluging your device: if it's detected, you'll find its information (here you have an example for an USB dongle):

[22401.292122] usb 1-4: new high-speed USB device number 5 using ehci-pci
[22401.484777] usb 1-4: New USB device found, idVendor=8564, idProduct=1000
[22401.484787] usb 1-4: New USB device strings: Mfr=1, Product=2, SerialNumber=3
[22401.484793] usb 1-4: **Product: Mass Storage Device**
[22401.484799] usb 1-4: **Manufacturer: JetFlash**
[22401.484805] usb 1-4: SerialNumber: YU3XUAOU
[22402.067734] usb-storage 1-4:1.0: USB Mass Storage device detected
[22402.067933] scsi2 : usb-storage 1-4:1.0
[22402.068273] usbcore: registered new interface driver usb-storage
[22403.073152] scsi 2:0:0:0: Direct-Access     JetFlash Transcend 32GB   8.07 PQ: 0 ANSI: 2
[22403.075508] sd 2:0:0:0: Attached scsi generic sg1 type 0
[22403.081832] sd 2:0:0:0: [sdb] 62750720 512-byte logical blocks: (32.1 GB/29.9 GiB)
[22403.084928] sd 2:0:0:0: [sdb] Write Protect is off
[22403.084938] sd 2:0:0:0: [sdb] Mode Sense: 03 00 00 00
[22403.086767] sd 2:0:0:0: [sdb] No Caching mode page found
[22403.086776] sd 2:0:0:0: [sdb] Assuming drive cache: write through
[22403.091701] sd 2:0:0:0: [sdb] No Caching mode page found
[22403.091712] sd 2:0:0:0: [sdb] Assuming drive cache: write through
**[22403.883752]  sdb: sdb1**
[22403.886794] sd 2:0:0:0: [sdb] No Caching mode page found
[22403.886804] sd 2:0:0:0: [sdb] Assuming drive cache: write through
[22403.886812] sd 2:0:0:0: [sdb] Attached SCSI removable disk

Here my device is /dev/sdb, and contains one partition (/dev/sdb1). Your device names may vary of course.