Stephen Carlson recently linked to a new online edition of Papias fragments. The new collection of fragments was put together by Tom Schmidt and some other individuals he mentions on the page just linked. It's the best collection I've seen yet. He includes some material that he doesn't believe has ever been published in English before, and he includes some translations of his own and corrections of previous translations. There's a lot of significant material there.
When I linked to an older collection of Papias fragments in the past, I noted that every source who comments on Papias' relationship with John either states or suggests that he had met the apostle. I think the same is true with this latest collection of fragments, which is the most complete one I've seen. The modern dispute over Papias' relationship with John is often framed as if we have to judge between two sources, Irenaeus and Eusebius of Caeserea, often with the suggestion that Eusebius is the more reliable of the two. Not only is the suggestion that Eusebius is the more reliable source on this matter dubious, but it's often not mentioned that other sources commented on the issue as well and supported Irenaeus' position. Eusebius himself was inconsistent on the issue. He affirms Irenaeus' view in another passage. Thus, every source to comment on the issue suggests that Papias met John, and one source is inconsistent on the matter. And the reasons Eusebius gives for doubting Papias' close relationship with John are dubious, for reasons I've mentioned before. There's no good reason to doubt that Papias met John.
The Papias fragments, as well as Tom Schmidt's comments on them, also contain some other significant information, such as Papias' affirmation of the authenticity of the book of Revelation and a report by some sources that Papias was the secretary who wrote the fourth gospel at John's dictation. I recommend reading all of the fragments and the commentary on them.
We may find a copy of Papias' work someday. It was still extant in the Middle Ages, but was eventually lost.