Try the below code for your requirement.

Apex Controller : This controller to get the Account id from the page block table when user click it and it will display the list of contacts associated with that particular contact

public with sharing class DisplayContact {
    public List<Contact> conList {get;set;}
    public DisplayContact(ApexPages.StandardSetController controller) {

    }
    
    public PageReference ContactLists()
    {
    if(ApexPages.currentPage().getParameters().get('id') != null)
      conList = [Select id,Name,Phone,Email from contact where accountId =: ApexPages.currentPage().getParameters().get('id')];
     return null;
    }   

}



Visualforce : Visualforce page to display all the acocunt record and its contact record. For the partical page refresh we used rerender concept in the visualforce page
 
<apex:page standardController="Account" recordSetVar="accounts" tabstyle="account" sidebar="false" extensions="DisplayContact" >
  <apex:pageBlock title="Account" >
    <apex:form >
      
      <apex:pageBlockTable value="{!accounts}" var="a" id="list">
      
        <apex:column headerValue="Account Name">
        <apex:commandLink rerender="contactDetails" value=" {!a.Name}" action="{!ContactLists}">
         
         <apex:param name="id" value="{!a.id}"/>
       </apex:commandLink> 
         </apex:column>
        <apex:column value="{!a.type}" />
        <apex:column value="{!a.billingstreet}"/>
        <apex:column value="{!a.billingCity}" />
        <apex:column value="{!a.billingCountry}" />
        <apex:column value="{!a.billingPostalCode}"/>
        <apex:column value="{!a.createdById}"/>
      </apex:pageBlockTable>
     
    </apex:form>
   
  </apex:pageBlock>
  <apex:pageBlock title="Contact">
   <apex:outputPanel id="contactDetails">
     <apex:pageBlockTable value="{!conList}" var="con" id="conlist" title="Contact">
     <apex:column value="{!con.Name}"/>
     <apex:Column value="{!con.Phone}" />
     <apex:Column value="{!con.Email}" />
     </apex:pageBlockTable>
        
  
    </apex:outputPanel>
  </apex:pageBlock>
  
</apex:page>