1. Various insects have limitations on how often they reproduce or the female always lays eggs after fertilization, regardless of if the male was fertile at all, causing infertile or inviable eggs to form.
2. Insects have chromosomes specific to their sex, similar to the XY System in Humans but the X0 System (ie, lack of an X chromosome is a male) is a bit more popular in this kingdom (IIRC).
3) Radiation can be very targeted, you just need a method of aiming, a computer can probably do it. Or you can abuse feeding habits. Ie, you make it so that the insect can only feed in a specific position, then beam radiation at a fixed spot which will be close enough.
Radiation cannot be targeted precisely enough to affect individual parts of a mosquito. Even if you could somehow collimate a small enough beam, controlling the energy and modelling the mosquito so that the Bragg peak (point of maximum energy deposition along the beam axis) is where it should be, is not currently possible.
For example look at one of the most precise applications so far, proton beams for ocular cancers (e.g. Paul Scherrer Institute in Switzerland). The modelling required to calculate the correct energy is non trivial and with large uncertainties, and compare the size of an eye to a mosquito.
Additionally, individually doing this for millions of mosquitoes is not possible right now
You don't have to aim it at a point, a line is good enough. A cyclotron should be sufficient to generate a disk-shape of radiation, which could be aimed downwards, via Bremsstrahlung. You could aim that just outside feeding places so that the backside of the mosquittos remain exposed, should be possible to do that on a large scale to make millions of them. You can make it easier if you consider that it's sufficient if their offspring is infertile and reduce the dose for the initial generation, then just blast the followup generation with a general dose.
2. Insects have chromosomes specific to their sex, similar to the XY System in Humans but the X0 System (ie, lack of an X chromosome is a male) is a bit more popular in this kingdom (IIRC).
3) Radiation can be very targeted, you just need a method of aiming, a computer can probably do it. Or you can abuse feeding habits. Ie, you make it so that the insect can only feed in a specific position, then beam radiation at a fixed spot which will be close enough.