The second data release of Gaia revealed a parallax zero-point offset of -0.029mas based on quasars. The value depended on the position on the sky, and also likely on magnitude and colour. The offset and its dependence on other parameters inhibited improvement in the local distance scale using for example the Cepheid and RR Lyrae period-luminosity relations. Analysis of the recent Gaia Early Data Release 3 (EDR3) reveals a mean parallax zero-point offset of -0.021 mas based on quasars. The Gaia team addresses the parallax zero-point offset in detail and proposes a recipe to correct for it based on ecliptic latitude, G-band magnitude, and colour information. This paper presents a completely independent investigation into this issue focusing on the spatial dependence of the correction based on quasars and the magnitude dependence based on wide binaries. The spatial and magnitude corrections are connected to each other in the overlap region in the range 17