Yes, you can use an FE lens on an E-Mount camera that has an APS-C sensor. The image circle of a FE lens is larger than the image circle of an APS-C size sensor. Therefore, only the centre of the lens is used to capture the image.
Due to the smaller image circle of the sensor, the field of view changes compared to using a FE lens on a Full Frame camera and therefore the focal length extents by factor 1.5. E.g. when using a FE 50mm lens, the focal length and the field of view on APS-C size sensor will be equivalent to a 75mm lens.