Help identifying a transformer with yellow bobbin and clarifying its purpose
Mosquito taser, here's a possible circuit solution:



Source: this forum

The transformer is used to make a high voltage from the 3 V supplied by the batteries. The transformer also provides feedback to the transistor so that it starts oscillating which is needed to make AC from the DC of the batteries. Transformers only work on AC so that's why that is needed.

Making the transformer part of the oscillation circuit also helps in cost saving (now only one transistor is needed) and also making sure maximum power is put through the transformer as it will saturate and that partly keeps the oscillation going.

These transformers usually do not have any part numbers, they're made for this purpose (bug zapper) only. They might even be made to order, the bug zapper manufacturer just tells the transformer factory what it needs and how many.