There has been a lot of rubbish about some remnant non-avian dinosaur clades surviving into the early Paleocene, but is that true? The short answer is a resounding "NO!", but a little context never hurts. These claims are mostly based off of a reworked hadrosaur leg fossil found in early Paleocene deposits.
"Reworking" in a geological/paleontological sense happens whenever a river cuts into old deposits and mixes the old material with the new, thereby explaining how a hadrosaur leg bone got mixed in with early Paleocene sediments, and this has also been forwarded as an explanation for the Bug Creek formation found out west in the Dakotas, wherein Paleocene-age fauna were found mixed together with late Cretaceous age fauna, thereby providing a plausible explanation for how something like Protungulatum or Purgatorius got mixed up with Tyrannosaurus and Triceratops fossils.
A good covering of this rubbish of Paleocene dinosaurs can be found here.