Fujifilm X-T20 has a Fujifilm X lens mount and currently there are 84 native lenses available for this mount.
The latest released lenses that are compatible with the X-T20 are the Rokinon 8mm f2.8 Fisheye, the Fujifilm XF 8mm F3.5 WR and the Tamron 11-20mm F2.8 Di III-A.
Fujifilm X-T20 doesn't have a sensor based image stabilization system but 18 of these lenses already comes with optical image stabilization.
Since Fujifilm X-T20 has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on X-T20.
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Fujifilm X-T20 Lenses with Image Stabilization
Fujifilm X-T20 Lenses with Weather Sealings