Use a bit like this sized according to the screw size you plan on using and use a wooden plug not wood filler.
By using a wooden plug and paying attention to the grain in the threshold and in the plug once sanded off it will be near invisable, putty will stick out and not take stain like a wooden plug will.
By using a wooden plug and paying attention to the grain in the threshold and in the plug once sanded off it will be near invisable, putty will stick out and not take stain like a wooden plug will.