Two organizations have these supposed emails, Fox and NYPost. They could mathematically prove their legitimacy by simply posting the entire raw messages, with headers. DKIM was active at the time these messages were supposedly sent, so if the signatures match up, authenticity is confirmed.
The fact that this hasn't been done is concerning, unless it's being sat on for future impact.. the "drip drip drip" method of political bombshell news isn't a new tactic. If we're still here in a week with nothing other than screenshots, we can probably write the messages off as frauds. I'm withholding my judgement for a few days.