It is a transformer or choke if some sort. It will almost certainly be a special part for that specific power supply.
Are there any other connections that the two pairs of wires visible in the photo?
Definitely a complex and custom-made part, unfortunately.
Are you certain it is faulty? The driver transistors and other components usually (but not always) fail before transformers.
I am not sure it is faulty.
At times the power supply comes up and at times it does not come up.
when it does not power on i have noticed that the base pin of the driver transistor has full rated voltage 350v of the filter capacitors
while when working the base voltage is about 175v.
After discharging the capcitors it always power on.