You may soon be able to jailbreak iOS 12.3.1 thanks to the discovery of new tfp0 bug. Here are the details on it.
iOS 12.3.1 battery life drain issue includes fix for iOS 12.3 running iPhone, iPad and iPod touch devices.
You can now download iOS 12.3.1 IPSW links and OTA Update for your iPhone and iPad. Changelog and Release Notes are detailed here!