Best way to check if your Sony NP-FW50 battery is genuine is to call Sony support and they will be able to tell fakes and genuine batteries apart. With little effort you may also check your battery yourself. Below are few hints what you should look for.
1. Check your battery serial number using form on main page. It has list of known fake numbers and checks if number is in valid format. If validation says "known fake" you are out of luck. If some characters of serial number will be displayed in red color then they do not match valid format and most likely your battery is fake (there is also slight chance that serial number decoding algorithm needs an update).
2. If serial number validates correctly (or partially) and your battery has data matrix code on it you may use some bar code/QR code reader (ie. on your phone) to read that code.
Here is an example from genuine battery: 49942656GH1709270170265027
The part in red is manufacture date in format YYMMDD so this sample battery was manufactured on September 27th, 2017. Compare date from matrix code with date from serial number. Both dates should always be the same. If they are different you most likely have fake battery or someone has replaced sticker (rather unlikely) or battery has been tampered with in some other way.
Here are values of matrix codes from known fake batteries (they may have various serial numbers):
If your battery has one of those, its fake.
3. Older batteries have micro QR code instead of data matrix. Most fakes of such batteries can be identified by visually checking this code. If pixels in code are uneven, heavily rounded, bold, fuzzy, not sharp or otherwise not "perfect" then battery is most likely fake. Here is an example:
Be warned however that some genuine batteries have slightly rounded pixels in their micro QR codes. Also don't panic if micro QR on your battery is different but otherwise looks sharp. There are few variants of micro QR codes on genuine batteries.
4. Carefully inspect battery visually, especially sticker on the back. Check for print errors, wrong font, wrong letter spacing, different icons etc. If you have 100% genuine battery (for example one that came with your camera) use it for comparison and check if every little detail matches. Especially check serial number, it shouldn't be flat but engraved or convex.
5. Check weight of your battery and compare it with known genuine batteries.
6. Check gallery with images of genuine batteries and compare them with your battery. There are also other informations there that can be helpful.