Cannot use Disk Utility to create partition from free space on external USB drive
I think Disk Utility misses a proper EFI partition at the beginning of the disk.

If you don't want to completely erase the drive you should be successful following the steps below:


Open Terminal and enter the following to get an overview:

diskutil list


The 3 TB disk is your external disk. In the next steps I assume the disk identifier of your external disk is disk1
Get the block size of the external disk:

diskutil info disk1 | grep "Device Block Size"


In the next steps I assume that the Device Block Size is 512 bytes. If you get another block size (i.e. 4096 bytes) leave a comment.
Get the partition table of the external disk:

sudo gpt -r show /dev/disk1


The result is similar to the output below (your sizes are different though):

       start        size  index  contents
           0           1         PMBR
           1           1         Pri GPT header
           2          32         Pri GPT table
          34      262144      1  GPT part - E3C9E316-0B5C-4DB8-817D-F92DF00215AE
      262178        2014         
      264192  2244603904      2  GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7
  2244868096  2048002015         
  4292870111          32         Sec GPT table
  4292870143           1         Sec GPT header

Unmount the external disk:

diskutil umountDisk /dev/disk1

Now add a third partition with 

sudo gpt add -b 2244870110 -i 3 -s 1000000000 -t 48465300-0000-11AA-AA11-00306543ECAC disk1


I left some unallocated space (2014 blocks) between partition 2 and 3. 

The resulting partition table looks like this then:

       start        size  index  contents
           0           1         PMBR
           1           1         Pri GPT header
           2          32         Pri GPT table
          34      262144      1  GPT part - E3C9E316-0B5C-4DB8-817D-F92DF00215AE
      262178        2014         
      264192  2244603904      2  GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7
  2244868096        2014         
  2244870110  1000000000      3  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
  3244870110  1048000001         
  4292870111          32         Sec GPT table
  4292870143           1         Sec GPT header


You should choose a bigger size than 1000000000 blocks. The number of blocks has to be dividable through 8. The max size in my case would have been 2048000000 (1000000000 + 1048000001).
Now format the new partition with a file system and name the volume (in the example below Backup):

sudo newfs_hfs -J -v "Backup" /dev/disk1s3

Mount the volume and verify it:

diskutil mount /dev/disk1s3
diskutil verifyVolume /dev/disk1s3