If you have already tried rooting your Galaxy S4 mini 3G using the old method which requires you to replace your existing kernel with an insecure one first, you probably ended up being in a bad situation such as a bootloop. This is because you are trying to put a kernel based off Jelly Bean onto KitKat.
Also please keep in mind that the downloads included in this post are strictly meant for the GT-I9190 model only. You can check the Rooting category for guides on how to root the GT-I9192 and GT-I9195 (just make sure that the post begins with "(KitKat)" otherwise it is meant for Jelly Bean and you should not try it!).
- Working USB Cable
- CF-Auto-Root package + Odin - Click here to download.
- CWM Recovery 188.8.131.52 for GT-I9190 - Click here to download.
Rooting GT-I9192 running KitKat:
- Download the CF-Auto-Root + Odin package to your computer.
- Download the recovery package as well.
- Extract the CF-Auto-Root as well as the recovery zip files.
- Inside the CF-Auto-Root folder you should see Odin along with required files as well as a .tar.md5 file.
- Power off your phone and then begin holding the Volume down + Home + Power buttons together. Once you enter Download mode, press the Volume up button to have it say "Downloading..."
- Now connect it to your computer and start the Odin program
- In the Odin program, click on the PDA button and choose the .tar.md5 file that you got with the package.
- Click on the Start button and wait for the procedure to finish. After it is done, your phone should automatically reboot.
- Now repeat steps 5-6 and this time in the PDA field choose the recovery .tar.md5 file and click on Start.
- Your phone will once again reboot and you should have root access as well as a custom recovery installed.