Saurik, creator of Cydia just released an update to Cydia Installer to give support on iOS 8.3
To update cydia, you will just have to launch it and a pop-up will show up.
As noted in the changelog, on iOS 8.3, Cydia would report that it “cannot identify your device” while trying to access your account. This was due to changes on iOS 8.3, and has been fixed.
Also, this version of cydia installer supports file:/// Repository URLs
Recent versions of Cydia have rejected “local” repository URLs. This was due to an overly-limited filter on acceptable URLs. You can now again use local repositories.