Remote firmware update of MAX10 over a serial interface (like a serial boot loader)

You have a serious learning curve ahead of you. I know, I'm in the middle of a similar design. Things will get worse if you use the technique described in the link. It uses embedded Nios for serial communication and that has its own very steep curve.

Basically, you need two designs, one is your application and the other is a serial loader. Both reside in FLASH. The serial loader accepts data and programs your application code into FLASH. Then it boots your application. It's all very confusing and the documentation is poor. You'll need to do more searching, find some example designs that more closely resemble your own. Good luck.