Fujifilm X-T20 has a Fujifilm X lens mount and currently there are 149 native lenses available for this mount.
The latest released lenses that are compatible with the X-T20 are the Meike 56mm f1.7 X, the Sigma 15mm f1.4 DC C and the Meike 23mm F1.4 APS-C.
Fujifilm X-T20 doesn't have a sensor based image stabilization system but
22 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.
You may also also be interested in these:
Fujifilm X-T20 Lenses with Image Stabilization
Fujifilm X-T20 Lenses with Weather Sealings