These are instructions on how to root Samsung Galaxy S3 Mini GT-I8190 using pre-rooted Stock ROM (android 4.1.2 base-XXAMG1).
Requirements Your Samsung Galaxy S3 Mini GT-I8190 should have at least 30-40 percent of battery to perform the rooting process.
Root Samsung Galaxy S3 Mini GT-I8190 with Pre-Rooted Stock ROM
Step 1: Download and Install Samsung USB Driver on your computer. If in case, Samsung USB Driver is already installed on the computer then SKIP this Step.
Step 2: Download and extract the root files on your computer. After extracting you will be able to see the following files:

Step 4: Now, you have to enter into Download Mode on your phone by Pressing Volume Down Key, Home Button and Power key at same time for 5-8 seconds until you entered to the download mode.


Step 6: Now, Open Odin3 (found in the extracted folder, that you have downloaded in the Step#2) on your computer. Then connect your phone to the computer.


Step 8: Once your device detected by Odin, click on the PDA button and select the I8190OXXAMG1 PRE-ROOTED.tar file (you have extracted this file in step#2).


Step 9: Now, click on the Start button in odin to begin the Flashing. Once flash process is completed your phone will restart automatically.



Optional You can also verify the root status of your device by using the Root Checker App.
Notes
[*] Data Loss Process Flashing Pre-Rooted Stock ROM is always a data loss procedure. So, always take backup of your personal data before flashing the Stock ROM.
[*] Warranty Void Your Samsung Galaxy S3 Mini GT-I8190 Warranty may be Void after following the above tutorial.
[*] How to Unroot? To unroot Open SuperSU > Settings > Full Unroot.
[*] Samsung Stock Firmware If you are looking for the original firmware for your device, then head over to Download Samsung Stock Firmware page.
[*] Samsung USB Driver If you are looking for the original USB Driver for your device, then head over to Download Samsung USB Driver page.
[*] Credits The Pre-Rooted firmware used in this tutorial is made available by Avicohh (xda developer). Very thanks for the firmware, without it the above tutorial was not possible.