Hi and Welcome to LQ!
GParted will make the partition as you've done, you also need to make a file system.
Since you're using ext4, the command you'd want to use would involve being root or using the sudo command:
$ sudo mkfs.ext4 /dev/sdc4
Once the file system is created, you need to mount it, typically you create a directory for mounting in the /media tree:
$ sudo mkdi /media/anyname
$ sudo mount -t ext4 /dev/sdc4 /media/anyname
This should mount the file system under /media/anyname. You can continue to use sudo to manipulate ownership and group. A good thing to check is to see what group the user "Person" is, typically this is also "Person". For instance if I make a user "frank", it typically also has a group "frank". My point there is the next set of command are to change the owner and group of the file system to match your user "Person".
$ cd /media/anyname
$ sudo chown -R Person *
$ sudo chgrp -R Person *
This changes recursively down sub-directories -R (not that you need it with a new file system and nothing yet under it), all file ownership (chown) to be owned by the user "Person", and next changes the group (chgrp) for all files in the file system to belong in the group "Person".
At this point you should be all set and files should be accessible by user Person.