The word "fawn" can mean two different things. As a noun, it refers to a young deer. As a verb, it means to overly praise or flatter someone, usually in an insincere way. Full definition
It doesn't make you look as good as you might think, even though you do get a lot of folks over there fawning over you. (realclimate.org)
(laughs) The secret is to give cats the space they need, and to let them come to you instead of fawning over them. (petsmagazine.com.sg)
Some boxers are classified as «reverse brindles,» where the dark hairs are the predominant appearance, with fawn coloring a minor or background part of the coat color. (dogcare.dailypuppy.com)