Let me correct a bit on what Rocky said. FIR in cognizable crimes can be lodged in any Police Station. If the offence is not done in the area of jurisdiction, ZERO FIR is lodged and the same is sent to the Police Station of competent jurisdiction.
However, you have to show appropriate reason to lodge an FIR in any other Police Station.
And there is a certain time lapse between the transfer of case, which can extend to years. In one particular case, I know of. It has not reached the other PS in last 6 years.
It is better to lodge the complaint in PS where the crime was committed, that is place Y in your case.
Regards,
If you don't fight for what you want, don't cry for what you LOST.