Can someone identify this bird?
It looks like a passerine bird, but I can't really tell the species without seeing the whole body. As for what to do with it, your best course of action is to leave it alone. Trust me. Once placed tissue paper over a pigeon's eggs to keep them warm, and the mother crushed them when she landed on the nest because she didn't see the eggs.

If there are eggs in the nest, try noting down what color they are. Passerines have colored eggs.