Exoplanet Kepler-1625 b is a gas giant orbiting a G-type star in a relatively wide 287.38 days-long orbit. It was confirmed in 2016. Recently the HEK project (Hunt for Exomoons with Kepler) reported a new discovery - first significant exomoon candidate, orbiting this planet. Despite on only 3 transits that was observed, the exomoon signal could be clearly seen on the light curve, blending with the parent planet's signal:
Calculation shows that moon is a Neptune-sized body (!) separated by a 19 planetary radii from its parent planet. Uncertainty in the radius of the parent star is high (some recent works increased it 2 times compared to 2016 data), so both planet and moon could have significantly different radius than provided. But the parent planet's mass was derived from photometry, and being approximately 10 Jupeter's masses. This increases probability of existence of such a large moon.
Link to the scientific article.
The next transit of this system is expected in October 2017, and the team requested the time on the Hubble Space Telescope.
Addon for SE 0.980:
Screenshot of the planet and its moon transiting the disk of the parent star (0.981):