A fossil named Castorocauda lutrasimilis, meaning beaver-tailed (Castor is the genus for Beavers) is also otter-like (Lutra is the genus for otters). The scientists who named the fossils are paying homage to the fact that one feature, the tail looks a bit like a beaver, and the habit and diet of the animals seems a bit like a river otter. It was sometimes called the "Jurassic beaver" by some popular press articles though they noted it was also like an otter and a platypus. Does than mean that this animals was "like" a modern mammal. Well, I suppose it was but only in the sense that flying squirrels are like marsupials because they have some features similar to sugar gliders or that the Ichthyosaurs of the Jurassic are called the dolphins of the dinosaur age because they have some features of dolphins despite being reptiles rather than mammals.
So, no, there is no evidence to date that an organism related to a beaver or any other rodent form is found preserved alongside dinosaurs. Yet many creationist speakers say that modern mammals such as beavers have been found with dinosaurs. Carl Werner, the originator of the idea that fossil evidence of beavers with dinosaurs may have been found does, at times, ad the caveat that it looks like (spoiler alert - no it really doesn't other than in a very superficial way) or similar to modern beavers but, well, let me allow him to put it in his own words from an interview on Creation.com: “At the dinosaur dig sites, scientists have found many unusual extinct mammal forms such as the multituberculates2 but they have also found fossilized mammals that look like squirrels, possums, Tasmanian devils, hedgehogs, shrews, beavers, primates, and duck-billed platypus. I don’t know how close these mammals are to the modern forms because I was not able to see most of these, even after going to so many museums.”
Here Werner adds the caveat that he does not know how close these mammals are to the modern forms. He says he was unable to see most of these fossils. However, he had access to the research paper describing these fossils and the "beaver" in particular. In this video we look at that very paper and you will see that this paper makes it clear it is not closely related at all to beavers or rodents in general. Werner should know that rather than saying he can't know how close they are to other mammals he absolutely should know if he had done his homework.

Article discussed: https://www.science.org/doi/10.1126/s...
00:00 The Jurassic Beaver Controversy
03:52 Analyzing the Original Research Paper
09:52 Anatomy of the "Beaver-like" Fossil
15:55 Size Matters: Comparing Ancient and Modern
21:41 Teeth Tell the Tale
27:56 Misleading Claims and Audience Perception
37:29 The Importance of Accurate Communication
47:01 Evaluating Scientific Integrity
52:45 Final Thoughts on Fossil Interpretation
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Joel Duff (aka Dr. Duff or The Natural Historian) resources:
About: https://joelduff.org
Blog: https://thenaturalhistorian.com
Twitter:   / naturalhistoria  
Facebook:   / thenaturalhi.  .
Photography "Portraits of Creation:" https://www.beechnutphotography.com/
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