Hi Mohammad,

Can you try the below code and check:

>> public with sharing class AccountController1_picklistrendering {
    public String selectedAccId{get;set;}
    public String selectedConId{get;set;}
    public list<contact> conlist{get;set;}
      
          public List<SelectOption> getAccountNames() {
                  List<SelectOption> accOptions= new List<SelectOption>();
                  accOptions.add( new SelectOption('','--Select--'));
                  for( Account acc : [select Id,name from Account ] ) {
                          accOptions.add( new SelectOption(acc.Id,acc.name));
                  }
                 return accOptions;
           }
         
      public void getContactNames()
{
    conlist = [select id,firstname,lastname,email,accountid from contact where accountid=:selectedAccId];
    system.debug(conlist);
    
}
    }

>> <apex:page controller="AccountController1_picklistrendering">
   <apex:form >
      <apex:pageBlock title="Account Name">
            Account Names&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

             <apex:selectList value="{!selectedAccId}" size="1">                                 
                <apex:selectOptions value="{!AccountNames}"/>
                <apex:actionSupport event="onchange" reRender="a"/>
             </apex:selectList>

             <br/><br/>

           Related Contact Names&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

            <apex:pageblock >
   <apex:pageblockTable value="{!conlist}" var="c" id="a">
       <apex:column value="{!c.firstname}"/>
       <apex:column value="{!c.lastname}"/>
       <apex:column value="{!c.email}"/>
       <apex:column value="{!c.accountid}"/>
   </apex:pageblockTable>
</apex:pageblock>

       </apex:pageBlock>               
    </apex:form>
</apex:page>

In case if it helps can you please choose this as the best answer so that it can be used by others in the future.

Regards,
Anutej