Mysterious bits of wood

There seems to be a rain of sawdust in our backyard. But the affected is only the spot where the slippers are resting. It is exactly at the bottom where the edge of the roof is. So if there is something at the edge of the roof that could fall then it is it. It is not an ordinary sawdust but definitely bits of wood or of similar material.  

When something that cannot be explained is found on the ground, the usual suspicion is the birds. Maybe it is the work of the birds. But yesterday, the same dirt was there and it was already cleaned. This morning there was again that dirt that looks like sawdust. That means something alive is doing that. The roof has no trace of anything, intact and no damage at all. So what is that mysterious bits of wood? I still have no answer as of now.