Hi Commnunity, 

I was able to complete a customized 'CaseEmailExtension' code solution in my SandBox, which queries a Case EmailMessages, and output these to a VisualForce Email Template.
I am struggling with adding the Tests, and would be glad to receive some help.
Below is the VisualForce Component:

<apex:component controller="CaseEmailExtension" access="global">
    <apex:attribute name="caseId" type="Id"  description="Case Id" assignTo="{!csId}"/>    
            <apex:repeat value="{!sortEmails}" var="email">
    <apex:outputText value="{0,date,dd'.'MM'.'yyyy HH:mm:ss z}" style="font-weight:bold;font-style:italic;font-size:15px;float:left">
                    <br><apex:param value="{!email.MessageDate}" /></br></apex:outputText>
                    <br>From: &nbsp; <apex:outputText value="{!email.FromAddress}"/></br>
                    To: &nbsp; <apex:outputText value="{!email.ToAddress}"/>
                    <apex:outputPanel rendered="{!email.CcAddress!=null}" >
                    <br>Cc: &nbsp; <apex:outputText value="{!email.CcAddress}"/></br></apex:outputPanel>
                    <apex:outputPanel rendered="{!email.BccAddress!=null}" >
                    Bcc: &nbsp; <apex:outputText value="{!email.BccAddress}"/></apex:outputPanel>
                    <br>Subject: &nbsp; <apex:outputText value="{!email.Subject}"/></br>
                    <br><apex:outputText value="{!email.HtmlBody}" escape="false"/></br>
____________________________________________
        </apex:repeat>
</apex:component>

And the Apex Class:
 

public with sharing class CaseEmailExtension {

public ID csId {get; set;}  // comes from assignTo on component 

public CaseEmailExtension() { }
    
private final Case currentCase;

public CaseEmailExtension(ApexPages.StandardController currentcase) {
    this.currentCase = (Case)currentcase.getRecord();
  }

  public List<EmailMessage> getSortEmails(){
  String contactEmail = [SELECT Id, ContactEmail FROM Case where Id=:csId].get(0).ContactEmail;
  contactEmail = '%'+contactEmail+'%';
    return this.csId == null
        ? new List<EmailMessage>()  // handles UI preview use case
        : [SELECT Id, FromAddress, ToAddress, BCCAddress, CcAddress, MessageDate, Subject, Incoming, HtmlBody, CreatedBy.Name   
            from EmailMessage where ParentId =: this.csId AND(FromAddress LIKE :contactEmail OR ToAddress LIKE :contactEmail OR BCCAddress LIKE :contactEmail OR CcAddress LIKE :contactEmail)
            order by MessageDate DESC ];
  }
}

Thank you.