Apple has stopped signing iOS 13.1.1 and all lower versions of iOS 13 meaning its no longer possible to downgrade to them on your iPhone. It has also stopped signing iOS 12.4.1., the last stable release of iOS 12.
With the company now no longer signing iOS 12 firmware, it is now not possible to downgrade your iPhone running iOS 13 to iOS 12.4.1.
Surprisingly, Apple continues to sign iOS 13.1 for the time being, though it has stopped signing iOS 13.1.1 and iOS 13 itself.
Apple rolled out a number of iOS 13 updates within a short span of time after the OS’s public release. The initial iOS 13 firmware was quite buggy which led Apple to do this. iOS 13.1.2 is comparatively bug-free and stable in nature so it makes sense for the company to stop signing all previous buggy releases of the OS.
As of now, there is no jailbreaking solution for iOS 13 but it is usually recommended that you stay on the lowest firmware possible of the latest iOS release if you want to jailbreak your iPhone or iPad. We might see a jailbreak tool for older devices like the iPhone 6s to iPhone X using the checkm8 exploit. In case that happens, the iOS version will likely not matter since its a bootrom exploit that Apple cannot patch via software.