Adjust the design for your actual needs. Do you need all the stuff that's actually on an Uno? Probably not if it is plugging into a motherboard.
For example, the reset switch, voltage regulator if 5V is available, the 3.3V regulator if you don't need to output that, perhaps the LEDs.
Maybe you want a crstal instead of a resonator. USB interface needed? Or will the motherboard take care of that? Want a uC with 2 serial ports and more memory?
www.cbas-usa.com in California can make all you need once you have a design.
I think they do turnkey as well. Or you have Digikey and your PCB supplier drop-shop parts right to cbas-usa.
If you want all IO pins on one edge, I have designed a card like that as well.
Surface mount or DIP processor?
etc.