With the attached file, it appears you mean column B! Column A already has a count in it.
Code:
Private Sub Worksheet_Change(ByVal Target As Range)
Dim rng As Range
Set rng = Target.Parent.Range("B2:B100")
If Target.Count > 1 Then Exit Sub
If Intersect(Target, rng) Is Nothing Then Exit Sub
If Target <> "" Then
With Target.Offset(, 6)
.Value = Time
.NumberFormat = "h:mm AM/PM"
End With
End If
End Sub