@echo off
rem The * at the end of the destination file is to avoid File/Directory Internal Question.
rem You can do this for each especific file. (Make sure you already have permissions to the path)
xcopy /Y "\\Oldeserver\storage\data\MyFile01.txt" "\\New server\storage\data\MyFile01.txt"*
pause
rem You can use "copy" instead of "xcopy "for this example.