You can get the download links and information about the most popular iOS 13.3.1 jailbreak or jailbreak alternative methods as follows.
Checkra1n Jailbreak released for iOS 13.3.1 jailbreak. Now it is available MAC & Linux version and Windows support will be added soon.. This is compatible with iPhone 5S to iPhone X only. If you are a jailbreak expert, you can try this method from Checkra1n official site.
Here are some of trusted jailbreak alternative methods for iOS 13.3.1 running all devices.
Hexxa plus is a trusted iOS 13.3 Jailbreak solution.
This will allow you to install Jailbreak / 3rd party apps by extracting repositories / sources.
It has thousands of Jailbreak and 3rd party apps / tweaks with these repos.
Bregxi is a newly introduced Jailbreak Repo extractor. It is compatible with the latest iOS 13.3.1.
It will install both Cydia and Sileo as well as other Jailbreak tweaks on your A12 iPhone or A12 X iPad.
You can extract many sources to get impressive features with Bregxi such as iOS themes, iOS launches, app stores, games and many more.