Pry the rotted wood from the sill with a cold chisel. Remove the paint from the frame around the damaged area by scraping it away with the cold chisel.
Form the sill's corners by drilling two ¼-inch pilot holes into the area where the sill's corners were. Soak the area around the holes in a consolidant, which is used to encapsulate the decay so it does not spread. Apply the consolidant by squeezing it onto the wood through a squeeze bottle. Soak the area until it no longer receives the consolidant. Drive screws into the pilot holes so they form each corner.
Allow the consolidant to become sticky. Coat a putty knife with lacquer thinner so the epoxy does not stick to it. Press epoxy filler over the corner screws with the putty knife. Apply more epoxy until it forms the sill's corner. Mold the epoxy with the coated putty knife to create the shape of the corner. Smooth the epoxy over the sill to reform the sill with the coated putty knife.
Let the epoxy dry to the manufacturer's recommendations. Smooth the epoxy with 100-grit sandpaper attached to a custom sanding block until it looks like the rest of the window frame.
Paint the repaired area with an exterior wood paint primer applied with a paintbrush. Let the primer dry to the manufacturer's' recommendations. Apply exterior wood paint over top of the primer with a paintbrush so the repaired area matches the existing window frame.