I'm looking for a word that refers to someone subservient in an overly attentive or annoying way.
marked by or exhibiting a fawning attentiveness
One possibility for this could be sycophant, which is a person who tries to win favor from the wealthy or powerful by flattering them. Other words for this idea are suck-up, brown-noser, or boot-licker - all of these cover the idea of a subservient individual trying to gain the favor of a powerful individual by doing certain things that the powerful individual will like. They capture the idea of being "overly attentive", as most people would not fawn over the powerful individual without such a motive. Other people usually find these attempts to curry favor as annoying, although the individual being served might enjoy the unquestioned subservience greatly.