Use the below methods to close the quick action popup and refresh the page from custom Salesforce Lightning Component.

$A.get(“e.force:closeQuickAction”).fire();
$A.get(‘e.force:refreshView’).fire();

 Sample code:

Lightning Aura Component:

Component:

<aura:component implements="force:hasRecordId,force:lightningQuickActionWithoutHeader" controller="Sample" >  
      
    <div class="slds-box slds-theme_default">   
        <ui:button aura:id="mybtn" class="slds-button slds-button--brand slds-size--1-of-1" label="Testing" press="{!c.onclick}" />  
    </div>  
      
</aura:component>  

Component Controller:

({      
      
    onclick : function(component, event, helper) {  
          
        var action = component.get( "c.firstMethod" );  
        action.setCallback(this, function(response){  
            var state = response.getState();  
            if (state === "SUCCESS") {  
                  
                alert( response.getReturnValue() );  
                $A.get( "e.force:closeQuickAction" ).fire();  
                $A.get( "e.force:refreshView" ).fire();  
                  
            }  
        });  
        $A.enqueueAction(action);  
          
    }  
      
})  

Apex Class:

public class Sample {  
  
    @AuraEnabled  
    public static String firstMethod() {  
        return 'Success';  
    }  
  
} 

Output: