you question is the flow code
public static void main(String[] args) {
    List<Integer> integerList = new ArrayList<>();
    integerList.add(1);
    integerList.add(2);
    for (Integer integer : integerList) {
        integerList.add(3);
    }
}
the error is that
Exception in thread "main" java.util.ConcurrentModificationException
    at java.util.ArrayList$Itr.checkForComodification(ArrayList.java:907)
    at java.util.ArrayList$Itr.next(ArrayList.java:857)
    at com.test.TestList.main(TestList.java:28)
we could use ListIterator to add the value.The code is this
package com.test;
import java.util.ArrayList;
import java.util.List;
import java.util.ListIterator;
/**
 *
 *
 *
 *
 * @author shikai.liu
 * @version 1.0
 * @since JDK1.7
 */
public class TestList {
    public static void main(String[] args) {
        List<Integer> integerList = new ArrayList<>();
        integerList.add(1);
        integerList.add(2);
        // for (Integer integer : integerList) {
        // integerList.add(3);
        // }
        ListIterator<Integer> integerIterator = integerList.listIterator();
        while (integerIterator.hasNext()) {
            Integer integer = integerIterator.next();
            if (integer == 1)
                integerIterator.add(5);
        }
    }
}
so your code is like that
ListIterator<Article> integerIterator = articleList.listIterator();
        while (integerIterator.hasNext()) {
            Article a = integerIterator.next();
            String checkId = "select * from article";
            PreparedStatement ps = conn.prepareStatement(checkId);
            ResultSet rs = ps.executeQuery(checkId);
            rs.next();
            if(a.getId()==rs.getInt("id")){
                //Here i'm returning list, just like it is in DataBase.
            } else{
                //integerIterator.add()
                //Here i want to add articles in the list
            }
        }