Is there a jailbreak yet for the iPhone 4S 6.1.3 software?

Is there a legit free jailbreak for it yet? Or at least a downgrade to 6.1.2?

There's no jailbreak available for your device running iOS 6.1.3. However, you could choose to downgrade your iOS to 6.1.2. I can't provide a link to iOS 6.1.2 due to legal issues, however, a google search should bring it up.

Once you have the file, open iTunes on the computer. Go to your iPhone 4S page, and hold shift while pressing restore. Choose the iOS 6.1.2 file, and wait for a while. This will make your iPhone 4S run iOS 6.1.2.

From there you can jailbreak your iPhone 4S by going to: http://evasi0n.com/ and downloading the "jailbreak-er" for windows, mac, or linux. Follow the onscreen instructions to jailbreak your iPhone 4S and you should be all set!

You can't downgrade to a lower iOS that the one that is being signed by Apple anymore.

As you're on a 4S with 6.1.3 you are stuck until iOS7 comes out.

Check here for all genuine jailbreaks; http://www.isthereajailbreak.com/