What kind of server do you want to run: a database server, a webserver, an active directory server, a print server, a file server, ... ?
Since you mention it would have to run the original OS, what server apps did you find in the Apples app store (for iOS), googles Play Store and Microsofts store for Windows mobile?
I am interested to see if there is a possibility in running a server from a cell phone (while still maintaining the original operating system). It is private information so I would like to stay away from 3rd party applications as much as possible. If this is not recommended, what are your suggestions for a home server. Any solution will have to be connected to a domain name. Thank you!