It's difficult to understand without context, but it sounds like a teacher asking pupils about the results of a test, and whether anyone has answered any more questions correctly. If so, it's OK English, but awkward. Better would be 'Who has answered more questions correctly?'

Hi Ed! Such a sentence would be used in a Biblical text or in Old English speaking and writing. In the old days many words would be cut out from sentences and rearranged. It was done to sound fancy and formal. The sentence “Has anyone more right?” translates to “Does anyone have more right?” in today’s English.

When you convert it to a sentence it would be "Anyone has more right".For me there is no such thing as "more right". It is best to say "more nearly right" or "closer to right" . You can be “almost right” but I don't think you can be “more right”.

Without context, it seems like a rhetorical question about the right of a person to do/think/say/have/etc. something, as if they are so deeply deserving of it that the question is posed to test the reader/listener to answer otherwise but arrive at the same conclusion.