How to save any file to iPhone

See this from the iPhone User Guide.

Files basics - Apple Support

That depends on where this file comes from or how you are accessing it.

For instance, Files sent over AirDrop should offer an App choice when received so you can decide what App to store them in.

Apps downloaded through Safari, will be saved in the Downloads folder in the Files app by default.

Files created in say Office 365 apps or Apple's Numbers, Pages or Keynote will saved to the corresponding folder in the Files App for the App that created them.

Beyond that, you really need to tell us where exactly you are getting these files from? What process you are following for these files