There is no definite answer to this question, as religious texts do not mention the killing of insects specifically.
So you are left to make your own value judgment as to whether you think killing a mosquito is a sin or not.
Most people would not consider killing a mosquito or any other insect a sin, I suspect, unless perhaps it was done with cruel or malice intentions.
In most cases, the killing of a mosquito is done in order to prevent suffering in other animals caused by the irritation of mosquito bites.
Mosquito bites can also be a health hazard as they can spread disease, and this must be taken into consideration as well.
