You haven't said how you copied the Fedora installer to the USB drive, and this detail is critical. Some tools (like Rufus) use normal partitions on the USB drive, but other methods (like using dd in Linux) create a Frankenstein's Monster sort of partition table. The reason is that many Linux installer .iso files are designed to work either when written to a USB flash drive (which requires a GPT or MBR partition table) or to an optical disc (which requires ISO-9660 or UDF data structures). These two sets of requirements are contradictory, but can coexist if various tricks are used. The result works, in the sense that the computer can read the disk either way and install the OS; but the resulting partition table on a USB drive is very non-standard and is likely to confuse normal partitioning software.
The solution is to do a better-than-normal wipe of the disk's data structures. If you can boot to a Linux environment, the following should do the job:
sgdisk -Z /dev/sdc
You must type this command as root, or using sudo; and you must change /dev/sdc to whatever the USB drive's disk identifier is. The -Z option to sgdisk should wipe the GPT and MBR partitioning data clean. You can then use fdisk, gdisk, parted, GParted, or whatever you like to re-partition the disk in a normal way and create a fresh filesystem on the resulting partition.
A more extreme approach is to completely wipe the disk:
dd if=/dev/zero of=/dev/sdc
This command is likely to take several minutes to complete, but it will write "0" values to every byte of every sector on /dev/sdc. (Change that identifier as necessary, of course.) This will guarantee that the disk is completely empty, whereupon you can re-partition it and begin using it. If it still doesn't work at this point, then the disk's hardware is probably failing. (It does happen -- and if you just wrote a whole Linux installer to the disk, that might have been enough to push it over the failure edge.)
If you're using Windows, there are equivalents to sgdisk and dd for it. I'm less familiar with Windows tools, though, so my lazy advice is to boot a Linux emergency disk to use sgdisk and/or dd. Somebody more familiar with Windows may be able to provide a more Windows-centric solution.
