Well... Not really possible to use this adapter.
The older MacBook Air's use the SATA dialog over a custom physical interface. Some folks created an adapter frame to convert the Apple custom physical connection to one a M.2 SATA based SSD unit could be used. Mostly this was due to the limits of the SSD's Apple offered at the time.
From my experience these adapters didn't do to well. The problem was most likely timing as Apple I think goosed the timing pushing the interface (device). As Apple controlled the device side they could get away with this unlike you who are going with some other vendors SSD which might not meet the timing requirements.
OK, lets get to the chase here... The newer 2013 onward MacBook Air systems use a proprietary PCIe 2.0 x2 interface (1 GB/s in each direction). In addition Apple altered the physical interface so the older adapter wont fit even if you got a PCIe M.2 SSD.
Your only choice is to get a SSD that was designed to work within this system. I would recommend you look at OWC SSD Flash Storage Upgrades for MacBook Air