The Code Like This:
JFrameT.java:
import java.awt.Color;
import java.awt.Dimension;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class JFrameT extends JFrame {
        private JButton testButton;
        private JPanel panelMain;
        private JPanelOne panel;
        public JFrameT() {
                // setting up JFrame
                setLayout(null);
                setPreferredSize(new Dimension(420, 90));
                setResizable(false);
                setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                // creating main JPanel (white)
                panelMain = new JPanel();
                panelMain.setBackground(Color.WHITE);
                panelMain.setBounds(0, 0, 420, 90);
                panelMain.setPreferredSize(new Dimension(200, 40));
                add(panelMain);
                // creating JButton in the main JPanel (white)
                testButton = new JButton("Button from main class");
                panelMain.add(testButton);
                // creating new JPanelOne object from JPanelOne class containing black JPanel
                panel = new JPanelOne();
                // adding black JPanel to main JPanel (white)
                panelMain.add(panel);
                pack();
        }
        public static void main(String[] arguments) {
                //Creat JFrame object and setting it visible
                JFrameT frame = new JFrameT();
                frame.setVisible(true);
        }
}
JPanelOne.java:
import java.awt.Color;
import java.awt.Dimension;
import javax.swing.JButton;
import javax.swing.JPanel;
import javax.swing.SwingConstants;
public class JPanelFirst extends JPanel
{
        public JPanelFirst()
        {
                // setting up black JPanel
                JPanel panel = new JPanel();
                panel.setPreferredSize(new Dimension(220, 40));
                panel.setBackground(Color.BLACK);
                // creating button on external JPanel
                JButton button = new JButton("Button (+JPanel) from external class");
                // adding button to the black JPanel
                panel.add(button);
                // adding blackJPanel
                add(panel);
        }
}
You can find it helpful more in this problem.