Yes, there are some alleged true accounts. For example, the story of John Titor. He claimed to be a time traveler from 2036. He made various predictions about future events and technology. However, many are skeptical as there's no conclusive scientific proof to support his claims.
Well, there are stories that some people believe might be true time travel accounts. One such is the Philadelphia Experiment. It was said that a U.S. Navy ship somehow disappeared and reappeared in another location, which some think could be related to time - space manipulation, though it remains controversial and lacks definite evidence.
There are a few stories out there. Some involve people who say they've had brief experiences of time travel. But most of these stories are difficult to verify. Scientists generally require more than just anecdotal evidence. These accounts often lack the necessary scientific rigor in terms of repeatability and measurement, so it's hard to say for sure if they are truly time travel.