throw new AuraHandledException('My Custom exception message');

try {

        //custom logic including dml operations

    } catch (Exception ex) {

  //logic to store log in custom object

        ErrorLog__c  errorLog=new ErrorLog__c();
        errorLog.Error_Date_and_Time__c=System.now();
        errorLog.Error_Line_Number__c=ex.getLineNumber();
        errorLog.Error_Message_c__c=ex.getMessage();
        errorLog.Error_Stack_Trace__c=ex.getStackTraceString();
        insert errorLog;

 //logic to notify aura component abt the exception

            throw new AuraHandledException(ex.getMessage());

        }