A clip of Jerry Springer has gone viral on Twitter, showing him reading a last will and testament with a bunch of juicy details ... and some fans think it's the real deal, but it turns out to be more fiction than fact.

The vid shows Jerry in a Zoom call, divvying up his assets to his children ... more specifically, leaving a good portion to 2 Black kids he had out of wedlock -- of course, this is in no way rooted in reality.

It's actually a pandemic-era virtual play called, "Blood Money." Jerry made a cameo in the production, which was featured in "REFRAMED 2020: A Festival of New Plays on Social Justice," presented by Tulane University ... the school where he once was a student.

It's a pretty interesting piece, but gullible folks online took it and ran ... with one saying, "Only Jerry Springer could go out like this."

Another person said Jerry "wrote" the best episode of his drama-filled reality show yet.

As if the evidence against this being legit wasn't enough, a source connected to Jerry tells us this obviously isn't real, adding he only had one daughter throughout his life.

You'll recall, Jerry was laid to rest earlier this month in a Chicago suburb ... after dying from pancreatic cancer.