Both Sony A77 and Nikon D3500 have 24.0 MP resolution sensors but Sony A77's sensor is APS-C (23.5 x 15.6 mm ) and Nikon D3500's sensor is APS-C (23.5 x 15.6 mm ).
Since Nikon D3500's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Sony A77.
One other difference between these two cameras that is worth mentioning is that Nikon D3500's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the A77 and D3500 sensor size comparison.
Sony A77 and Nikon D3500 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.