Of course you have to implement its own Checked/Unchecked Boolean Property in a custom Control, in this case a RadioButton. But the Checked Property must be implemented inside your custom UserControl not on different class.
You then can choose to use a Radibutton within your MyRadiButton control that derives from UserControl or you would do it using System.Drawing methods to paint a circle and draw text indicating the Text Property. This all is too difficult for a novice but you may find an example on Web.
Here is some code to start with:
Public Class MyRadioButton : Inherits UserControl
Private _Checked As Boolean
Property Checked As Boolean
Get : Return _Checked : End Get
Set(value As Boolean)
_Checked = value
EnableDisable(New PaintEventArgs(Me.CreateGraphics))
End Set
End Property
Sub New()
End Sub
Protected Sub EnableDisable(e As PaintEventArgs)
If Checked Then
Else
End If
End Sub
Protected Overrides Sub OnPaint(e As PaintEventArgs)
EnableDisable(e)
End Sub
End Class