I'm looking for small sized solo laptop motherboards like 3050, 4050, mx570, mx550 with motherboard size within 17cm*9cm for modding and developing mini Windows system handhelds, anyone have any clue?
There are plenty of companies doing this with Ryzen/RDNA based APUs. Even some people trying it with integrated Intel graphics. About the only way to get the battery life for a handheld. Having a discrete GPU is too power costly.
Such laptop motherboards will be relatively recent as well and cost quite a bit of money, pricing them well outside handheld territory.
The vast majority are going to be the full 13-15-17" wide so that they reach the I/O on both sides. Your best bet would be to look for boards that use daughter boards for I/O.