1. Set the DrawMode property of the Tab Control to OwnerDrawFixed. This property is decides whether system or developer painting the captions.
2. Add the code in the DrawItem event of the Tab Control – This event will be invoked for painting each Tab Page.

//This code will render a "x" mark at the end of the Tab caption.
e.Graphics.DrawString("x", e.Font, Brushes.Black, e.Bounds.Right - 15, e.Bounds.Top + 4);
e.Graphics.DrawString(this.tabControl1.TabPages[e.Index].Text, e.Font, Brushes.Black, e.Bounds.Left + 12, e.Bounds.Top + 4);
e.DrawFocusRectangle();

3. Now for close button action, we need to add the following code to the MouseDown event of the Tab Control.

//Looping through the controls.
for (int i = 0; i < this.tabControl1.TabPages.Count; i++)
{
    Rectangle r = tabControl1.GetTabRect(i);
   //Getting the position of the "x" mark.
    Rectangle closeButton = new Rectangle(r.Right - 15, r.Top + 4, 9, 7);
    if (closeButton.Contains(e.Location))
    {
        if (MessageBox.Show("Would you like to Close this Tab?", "Confirm", MessageBoxButtons.YesNo, MessageBoxIcon.Question) == DialogResult.Yes)
        {
            this.tabControl1.TabPages.RemoveAt(i);
            break;
        }
    }
}

Here is the screenshot, of the implementation, running on my machine.

Close Button in Tab Pages