first not sure if i need the paint event and second this code draw the points far on the form not in the picturebox not where i clicked with the mouse on the picturebox.

private void PictureBoxPoints_MouseDown(object sender, MouseEventArgs e)
{
    var coordinates = MousePosition;

    System.Drawing.SolidBrush myBrush = new System.Drawing.SolidBrush(System.Drawing.Color.Red);
    System.Drawing.Graphics formGraphics;
    formGraphics = this.CreateGraphics();
    formGraphics.FillEllipse(myBrush, new Rectangle(coordinates.X, coordinates.Y, 20, 20));
    myBrush.Dispose();
    formGraphics.Dispose();
}

private void PictureBoxPoints_Paint(object sender, PaintEventArgs e)
{
    // Do any additional painting needed on the PictureBoxPoints here
}