Wood putty to hold awning screws in rotten wood ?

Wood putty won't hold.

You need to find a way to add wood. Some have drilled the holes bigger and then glued in (using Gorilla glue or epoxy) some hardwood dowels to drill into. Others have moved the awning forward or backward a little to get to solid wood.

Others have added metal plates that are connected through the siding into solid wood and then mounted the awning hardware to the plate.