Maybe you could have the 01 or 02 of the project folder save to a variable when the project is created. Then somehow add that variable to the file when it is moved to the new folder.
Otherwise the serial number increments when it is used. So if you had a serial number for the part 01, 02, 03 ... 0n it would always want to use the next one when you access it.
Can you explain more on this with a example ?
I thought of a workaround but again my system is formatted , and it will take time to get fully functional. ( Have to setup the whole PDM base and all)
I don't think this is possible using the serial number functionality out of the box. That is designed to automatically increment and not reset just because the file is in a different folder.
To do what you want, you probably need to write an addin.