No problem ;D
What you will want is the untethered jailbreak.
I don't know much about IOS and jailbreaking as I've only used one apple product, the iPod
_______________________
Jailbreaking is complicated (sometimes).
And is dangerous if you don't know what you're doing.
_______________________
I don't think that jailbreaking supports IOS 6.1.3 fully at the moment.
My suggestion is you will need to downgrade to a lower IOS.
There is no problem is doing so because there really isn't much of a difference with the apple updates xD.
The thing is, apple says downgrading is not supported.
You know what? fuck apple
Everything is possible.
_______________________
I have had a look around and found out that jailbreaking the iPhone 4s is only compatible with every version of IOS except for yours.
They also say that it is impossible to downgrade.
________________________
I am not sure if this still works or not.
But look around for a backup of IOS 6.1.
Just plain old 6.1.
If you found and downloaded a backup.
Place it on your desktop or where ever.
Plug your iPhone in, load up iTunes and try find the 'restore' option.
And / or if you can, select the backup you downloaded.
This will trick your iPhone into thinking that it just restored your 6.1.3, but it actually installed the IOS 6.1 that you downloaded.
NOTE! Back up your phone before attempting any of this (using iTunes)
______________________
If all goes well you will have installed ios 6.1.
You can now jailbreak.
Preferably using evasi0n.
http://evasi0n.com/
Download the program for your operating system. (from the link I just gave you).
__________________________
Run / install it, follow the steps and cross your fingers
