Came across one issue that EDGE Server is not sending mails to Smart host as Smart host not accepting mails from the EDGE Server.
In Event EDGE Server, noticed the Certificate validation failure and Get-Exchangecertificate showed that Status: RevocationCheckFailure for the current certificate.
It happens when the EDGE Server not able to check the CRL path of the Certificate or some cached CRL can cause for this issue.
Hence delete the existing the cached CRLs and connect the EDGE Server with internet to download the CRLs again.
post that run Get-ExchangeCertificate and you can see that certificate Status is valid.