The checkra1n jailbreak has been updated with support for the Apple TV 4. The release was announced on Twitter by @nitoTV.
At this time the checkra1n jailbreak for tvOS only works on the fourth generation (HD) Apple TV. Support for the 4K Apple TV is possible but it will require a cable that doesn't exist yet and a reliable way to get into DFU mode. There are no ETAs on either.
If you have a 4K Apple TV that is jailbroken, stay on that firmware version.
Currently, there are no plans to bring checkra1n support to older Apple TVs but nitoTV is willing to lend a minor hand to anyone who wants to take on that project.
We'll be posted instructions for jailbreaking your Apple TV using checkra1n shortly. For now, check out the iOS instructions as there will be some similarities. ● How to Jailbreak Your iPhone Using Checkra1n
Please note that SSH isn't on port 44 and isn't enabled over USB. It's on port 22 in preparation for 4K support.