Ask the vet - Cat
Why is my kitten black along the sides of its nostrils?
Vet at FirstVet answers:
Kittens that have or have had a runny nose sometimes get a little black along the sides of their nostrils. It is nothing to worry about as long as the kitten seems well, is energetic, and is eating and drinking as usual. Remove any discharge around the nose so that air can easily pass through the nostrils. Usually the black discolouration goes away on its own with time.