I doubt a filler will hold screws, If you have the space, how about drilling out the screw holes to maybe 3/8ths inch and gluing dowels in them to take the new screw holes then filling in the rest with plastic wood before sand and finishing. Drill for the dowels as deep as you dare to give yiu plenty of gripping surface.
Even if you replaced the wood with a new chunk and could ,match the color, you'd want to put in some pins between tghe new and old wood to gain strength Tom
