You are trying to use down-level WinNT logons but specifying the domain fqdn.
Change this...
Start-Process powershell -Credential domain.com\Admin -password abc1234 New-DfsReplicationGroup -GroupName "RG01"
Invoke-Command -Credential domain.com\Admin -password abc1234 New-DfsReplicationGroup -GroupName "RG01"
To this... each of the below will autofill the password dialog with the user info, you still have to enter the password of course.
Start-Process powershell -Credential domain\Admin -password abc1234 New-DfsReplicationGroup -GroupName "RG01"
Invoke-Command -Credential domain\Admin -password abc1234 New-DfsReplicationGroup -GroupName "RG01"
Never put passwords in plain text in scripts
So, use
$DomainUserCreds = Get-Credential -Credential 'Domainname\Username'
Start-Process powershell -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"
Invoke-Command -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"
If you are logged on as a admin of the domain, you can just get this dynamically
$DomainUserCreds = Get-Credential -Credential "$env:USERDOMAIN\$env:USERNAME"
Start-Process powershell -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"
Invoke-Command -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"
If you domain is set to use UPN you can do
$DomainUserCreds = Get-Credential -Credential "$env:USERNAME@$env:USERDNSDOMAIN"
Start-Process powershell -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"
Invoke-Command -Credential $DomainUserCreds New-DfsReplicationGroup -GroupName "RG01"