NTFS partition on external HD not recognized or mounted on El Capitan or Sierra, even with latest Paragon or Tuxera
disk0s4 has the wrong GUID partition type - as visible in the Tuxera screenshot. The partition type is 48465300-0000-11AA-AA11-00306543ECAC which is HFS+ (the standard OS X partition type). You can check this by entering sudo gpt -r show disk0.

It should be EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 though, which is the GUID for Microsoft basic data partitions (BDP).

To change the partition type boot to Internet Recovery Mode or a second boot device (e.g. a thumb drive), remove disk0s4 with gpt and re-add it with the same boundaries (index number, beginning block &amp; size) but a different type.

Under certain circumstances - I need the output of sudo fdisk /dev/disk0 and some hexdump results additionally - unallocated disk space between disk0s3 and disk0s4 is required and the beginning block &amp; size have to be modified compared to your current gpt partition table.



Boot to Internet Recovery Mode or a thumb drive with either a full OS X install or an OS X Installer thumb drive. Editing the GUID partition table with gpt requires you to unmount the disk. You can't unmount the disk you are booted to.


Open Terminal (menubar Utilities > Terminal) and enter diskutil list to get an overview. Get the disk identifier of the 500 GB drive - this may be disk0 or disk1. Below I assume it's disk0. Use the disk identifier you have found in your environment though.

If you log-in as admin some commands require you to prepend sudo ... executing some commands (e.g. gpt). Booted to an installer thumb drive or to Internet Recovery Mode you are always root user and prepending sudo is not necessary. 
Get the partition table:

gpt show -r disk0

Unmount the disk

diskutil umountDisk disk0

Remove the 4th (falsely typified) partition:

gpt remove -i 4 disk0
diskutil umountDisk disk0

Your hexdump results ("eb 52 90 4e 54 46 53 20" is the "string" ∂RENTFS(x20)) show that disk0s4 has special NTFS Boot Sectors (which typically occur in the first and the last block of an NTFS volume) in block0 and block 121948143. (x0000000 is byte/block 0 of disk0s4 and xe898fde00 converted with a hex2dec service is byte 62437449216 or 62437449216/512: block 121948143). This shows that there is no gap between disk0s3 and disk0s4 and the size is (121948143 blocks + block0) 121948144 blocks.
re-add the 4th partition with a proper type but the old other values:

gpt add -i 4 -b 488722456 -s 121948144 -t EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 disk0

reboot