You need to be sure that your screws are long enough to 'grab' about 3/4" of the stud behind the jam. Countersink and fill the hole w/putty, and either paint or stain. If you're staining, mix some of the stain w/the putty as you 'roll' the putty between your fingers. Err on the light side if you're not sure how much to use. If you're painting, you needn't do anything but prime when it dries.