ABSTRACT When a black hole accretes close to the Eddington limit, the astrophysical jet is often accompanied by radiatively driven, wide-aperture and mildly relativistic winds. Powerful winds can produce significant non-thermal radio emission via shocks. Among the nearby critical accretion quasars, PDS 456 has a very massive black hole (about 1 billion solar masses), shows a significant star-forming activity (about 70 solar masses per year), and hosts exceptionally energetic X-ray winds (power up to 20 per cent of the Eddington luminosity). To probe the radio activity in this extreme accretion and feedback system, we performed very long baseline interferometric (VLBI) observations of PDS 456 at 1.66 GHz with the European VLBI Network and the enhanced Multi-Element Remotely Linked Interferometry Network. We find a rarely seen complex radio-emitting nucleus consisting of a collimated jet and an extended non-thermal radio emission region. The diffuse emission region has a size of about 360 pc and a radio luminosity about three times higher than that of the nearby extreme starburst galaxy Arp 220. The powerful nuclear radio activity could result either from a relic jet with a peculiar geometry (nearly along the line of sight) or more likely from diffuse shocks formed naturally by the existing high-speed winds impacting on high-density star-forming regions.