You may also need to investigate the skip certificate check plugin to see if certificate checking needs to be disabled for all of Jenkins. I believe there are portions of the git-plugin and/or git-client-plugin which use Java's certificate validation facilities directly.

Installed the plugin, same issue.

It works with a public GitHub repository, but not with my GitLab instance, and the issue is not related to credentials (tried keys and username and password).

The Jenkins version I use is Jenkins ver. 1.559 and it is under Windows (shamefully), I am running it for testing purposes with default basic configuration.

There is a posting on stackoverflow which provides more detail and may offer some hints of changes you could make to your configuration to avoid the problem.

In the current version (as of today: 1.2.1, not in jenkins-ci updatecenter yet) there is an option to ignore ssl-certs.

I don't see a change in the git-plugin source code which provides any option to ignore SSL certificates. Are you sure it is there?

Any update on this? I'm getting the error...

Failed to connect to repository : sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target

...even with http.sslverify set to false.

Is there a good workaround or fix for this issue available yet?

You might consider the comment in JENKINS-23050 which recommended a work around from Erik Zaadi's blog