Export PNG square with 1024km2

This is an interesting questions. If you are looking for a web service that lets you do that easily, there is none; you will have to run some calculations by yourself. Note that the map projection governs whether what is a square on the ground of the Earth ellipsoid is also a square in the resulting two-dimensional image; you don't say if you need a square PNG (but don't need a square patch of Earth), or if you need a square patch of Earth (but not necessarily a square PNG).

So your question has two parts, first: how to determine the coordinates of the four corners of this area (depending on projection and whether you need a square on Earth or a square result); second: how to export an area with known coordinates from OSM.

The first question is not OpenStreetMap specific and you will likely get better responses on a general GIS forum or Q&A site.

The second question has a number of different answers. If the EPSG:3857 map projection works for you, then you can use OSM's own image exporter (on www.openstreetmap.org, the icon on the right hand side of the map that shows an arrow pointing out of a box). It lets you select the four corners of the export area on the map but if you use your browser's network debugger you can see the request it generates and generate such a request yourself with the exact coordinates you have computed. Another option, especially if you are interested in different projections, might be one of the free third-party WMS servers from https://wiki.openstreetmap.org/wiki/WMS.