As you're only doing a straight -eq match on sAMAccountName you don't need to use -Filter, the Identity param will accept this along with other inputs:
- A distinguished name
- A GUID (objectGUID)
- A security identifier (objectSid)
- A SAM account name (sAMAccountName)
(documentation link)
Which makes your code very simple:
$User = Get-ADUser -Identity $Userid
To simplify it even further, you don't even need to use Get-ADUser at all!
Add-ADGroupMember -Members (link) accepts the same parameters as I mentioned for Identity ...
So you can use $UserID directly:
param($Userid,$AdditionalGroup)
Add-ADGroupMember -Identity $AdditionalGroup -Members $UserID