It is very unlikely that a mosquito can get drunk or feel the sense of alcohol impairment that humans and other animals do. Many times it is assumed that if a mosquito bites a drunk person, the mosquito will get drunk off of the alcohol in the blood of that person.
But the actual amount of alcohol in a drunk person is very small and the way this alcohol is digested in the body of a mosquito is not going to get it drunk. The blood-alcohol content of a person who is drunk is quite miniscule, and will not have the effect of getting the mosquito drunk.
To be legally drunk, a person needs to have only a .08% blood-alcohol level in most states, and this is quite a small amount when it is digested by the mosquito. In addition, the mosquito’s main diet consists of nectar and other sugary drinks, and it would not consume alcohol directly, which would be required for a mosquito to get drunk.