Unfortunately, a USB memory stick or USB SSD cannot be used for recording.
However, the USB HDD recording (REC) function is available on Sony's Android TV*. For more information, please visit the following FAQ: USB connectivity for Sony's Android TV.
NOTE: HDD REC and Satellite features are not available if YouView functionality is enabled. YouView on Sony TVs will offer consumers a consistent and easy to use YouView experience, including scroll back, search, discover and catch up TV (BBC iPlayer, ITV Player, All 4 and Demand 5). YouView functionality includes access to all the normal free-to-air channels via the YouView guide and mini-guide.