Q: My new iphone serial number does not exist in apple check coverage ? What that means?

How long have you had it?

Wait a few weeks and if you don;t see it, then contact Apple and ask about it.

Not necessarily. Depending on where you purchased it, it may take a few days to make its way into the database. If iTunes recognizes it, and the warranty check doesn't say it's been 'replaced', I wouldn't worry too much. It's a holiday weekend in the US right now.