When you get the dragged file name, pass it to a procedure to open it and read its contents and put inside the listbox.

Try this
Code:
Private Sub Form_OLEDragDrop(Data As DataObject, Effect As Long, Button As Integer, Shift As Integer, X As Single, Y As Single)
    Dim j As Long
    If Data.GetFormat(vbCFFiles) = True Then
        If Not (GetAttr(Data.Files.Item(1)) And vbDirectory) Then
            ' To open only one file
            OpenFile(Data.Files.Item(1))
            
            
            ' To open multi files
            'For j = 1 To Data.Files.Count
                ' OpenFile(Data.Files.Item(j))
            '    MsgBox Data.Files.Item(j)
            'Next
        End If
    End If

End Sub

Private Sub OpenFile(ByVal strFile As String)
    Dim intFN As Integer
    Dim strIN As String
    On Error GoTo errIOError
    intFN = FreeFile
    Open strFile For Input As #intFN
    Do While Not EOF(intFN)
        Line Input #intFN, strIN
        strIN = Trim$(strIN)
        If LenB(strIN) <> 0 Then
            List1.AddItem strIN
        End If
    Loop
    Close #intFN
    Exit Sub
errIOError:
    Close #intFN
End Sub