Is there an untethered jailbreak for the iPhone 4S 6.1.3 yet?

I can't tell which sites are legit. I remember checking like 2 months ago and just wanted to check again

No & there wouldn't be until iOS 7.

Actually there's no Jailbreak for i OS 6.1.3 release Yet, although you can try this one, which on publish this Blog, here some people says they already jailbreak their phone by fallowing this tutorial, i'm just sharing with you their thought

The only devices supported are 4, 3gs, and ipod touch and that is only semi-tethered, you have to wait it out

http://computersight.com/computers/tethered-jailbreak-for-ios-6-1-3-with-pictures-read-desc-first/