A car body repair putty called Bondo can be used for a weather resistant repair to almost any material -- wood, concrete, stone, steel, wood, plywood, etc. If the area remains wet constantly you may want to use a more expensive epoxy filler such as WoodEpox, West Systems, or Rot Doctor. But, if it just gets wet, say when it rains and then it dries, Bondo will do the job. Minwax sells Bondo as "Wood Filler," charging way too much for it. You can get Bondo cheap at auto parts stores.
It's a light gray plastic paste into which you mix a small amount of a maroon colored hardener which makes it set up in about 5 minutes, so you have to keep mixing small batches as you work. You can use an old slick paper magazine like Newsweek as a "pallet" to mix it on, and just keep ripping off the pages when the stuff sets up on them. Popsicle sticks or tongue depressors make good disposable mixers. The cured color is sort of a salmon pink.
You can use Bondo as an all purpose patcher where it will get painted over (it won't take stain). One common use is to repair door jams where they've rotted at the bottom. It holds up to to weather well, and grabs raw wood pretty tightly. You can help it stay put by giving it something to grab onto like drilling a couple of holes or driving some nails or screws "inside" the cavity you're filling. It doesn't shrink as it cures, and the fast setup means you can do the patch and be ready to take paint in less than ten minutes. Spread on a thin layer followed by sufficient product to fill the gap. Slightly over-fill to allow for sanding down. The stuff has a "green" stage in its cure cycle where it is stiff, but not yet rock hard. This is when you can carve/shape it with a Stanley Surform, rasp, or other tool quite easily for about 20 minutes after its sets up. Once it gets fully cured, you can shape it with sandpaper and files.
If you're repair won't get wet, I have used Durham's Rock Hard water putty to fill lots of cracks gouges, holes, etc.