Can you feed a baby bird in its nest?
It is not advised that you do. Please, don't feed baby birds that are in a nest.
If the mother witnesses or smells human presence in the nest she can actually abandon the chicks to die of cold or starvation. Aside from that, chicks can only really eat "mashed" food, basically food that has been chewed and regurgitated by their mother. By feeding the chicks you risk causing them to choke to death.
Never disturb nesting birds. You can however leave out soft, chopped fruit in your garden, such as grapes, pear, banana and apple. Then the mother will soften this and regurgitate it for her chicks. Please don't leave bread for chicks, because it can become trapped in their digestive tracts and probably kill them.
If however you notice the mother has not returned to the nest for a day or so, then you can call animal services to investigate and possibly rescue the chicks. Unfortunately a lot of mother birds are killed by cats, dogs, wolves or foxes while seeking food for their chicks.