I baked texture on a 4k image and I downscaled it to 512 using Gimp but the quality is bad in Unity 3D. The image format is png. Is it a good idea to bake texture on a 4k image and to downscale to 512 for mobile game? What can I do to keep a good quality on baked texture with small size (512 or below) for mobile game development?
In general, you can expect to sacrifice some texture quality if you use a smaller texture. It makes sense: with less data, something must be lost, and that's usually fine details and sharp edges. There are some strategies available, though, to get the most out of your texture data:
Make sure your model's UVs are laid out as efficiently as possible. Parts where detail is important -- like faces -- should be given more UV space than parts where detail is unimportant -- like low-frequency clothing or the undersides of models. Minimize unused texture space.
Where feasible, you can use overlapping UVs to reuse similar portions of your UV space. If your model is exactly symmetrical, you could map the halves to the same space. Or if your model is a crate with identical sides, you could map each side to the same UV square.
See if you can decompose your texture into multiple textures that are less sensitive to downsizing, then layer them together. For instance, a landscape texture might be decomposable into a low-frequency color texture and a high-frequency noise texture. In that case, the low-frequency texture could be scaled much smaller without loss of quality, while the high-frequency texture might be replaceable with a cropped, tiled texture, or procedurally generated in the shader.
Experiment with different resizing algorithms. Most image editors have an option to resize using bicubic or bilinear methods. Bicubic does a better job preserving edges, while bilinear can sometimes be a better match for some content/shaders. You may also be able to improve a resized texture with careful use of blur or sharpen filters.
If the hardware targeted by your game supports it, you should evaluate using hardware compression formats, like ETC2 or ASTC. The ETC2 format, for example, can compress 24-bit RGB texture data to be six times smaller while still having the same image dimensions. The compression is lossy, so some image information is lost and there are some artifacts, but for some content it can look better than raw textures rescaled to a similar data size. Depending on content, some combination of resizing and hardware texture compression may get you closest to your desired quality/size tradeoff. The Unity manual claims it automatically picks a good default texture format when exporting, but you can try other ones in the export options.
Usually, the motivation for using smaller textures is to consume less video memory and improve performance. However, if the motivation is simply to reduce the download size of the game, you could try alternate image formats. JPG, for instance, lets you choose an image quality value to get a smaller file size. It's rarely used for games, though, because it takes up as much video memory as a similarly sized PNG, can have artifacts, and doesn't support alpha.