How do i check a serial number

Unfortunately there is no central database or system for this sort of thing.

It is possible (but extremely unlikely) that you could contact Sony customer support and tell them your concerns and supply the serial number. If the original owner registered their device it is remotely possible that Sony could contact them and inquire if the device was sold, stolen or reported missing. However not everyone registers their devices and if it was never registered this wouldn't work.

This is an extreme longshot, however, unless you are talking about a professional studio camera worth tens of thousands of dollars. It is highly doubtful that Sony would want to get involved in tracking down the legitimate owner of a standard consumer device.

Another option is to call the police department (probably where the seller is located) and inquire if that device with that serial number has been reported as stolen.

If you are buying a used item and have even the slightest doubt about it being stolen the best advice is do not buy it. Buying a stolen device is an arrestable offense (Receiving Stolen Property) and, although unlikely, you could get in trouble for it if there was an investigation or the seller got arrested subsequently.

A price that is "too good to be true" is a bad sign. Trust your gut and, even though it might be something you really want, avoid it if it seems questionable.