Mails are not reaching to edge servers after properly configured Connector towards Edge server as well as receive connector on Edge server for Hub Transport server.
Found the Access denied error for SMTP Connections of hub transport server on Edge server. Also identified that mails are reaching to edge server as expected but returning back as edge server pushes it back with error Access Denied.
Identified that Send Connector on Hub transport server is using basic Authentications and also using some domain account account for authentication with edge transport server which is not available in edge server.
Since Edge server is not joined in domain and no domain users can authenticate with Edge server using Domain accounts. Thus created one local user account and added the uses to administrators Group. Added the user Account for basic authentication on Hub transport server and restarted the Transport service in Edge server. Now mails are delivered to edge server and edge server properly sends it to internet using send connector.