Why don't you try this on your device:
1. Press the Back Key while rebooting your device
2. First of all turn off your Samsung Galaxy S3.
3. After that turn on the device. When you see the boot animation logo start pressing the back key which is at right side of the device. Keep pressing untill your device successfully boot.
I hope this trick work for your Samsung Galaxy S3 too. In case this tip didn't work for you. You can check this tutorial for more tips:
https://www.whatswithtech.com/how-to-remove-exit-safe-mode-samsung-galaxy-s3/