There is only one file type that uses the .P2P extension:
FolderShare Placeholder File
A P2P file contains a shortcut to a file and is used by FolderShare, a Windows Live computer synchronizing service. It stores a reference to a specific file and is used in place of the actual file. P2P files are most often seen when On Demand Sync is active.
FolderShare was acquired by Microsoft in 2005. It allowed users to access information across various devices. By double-clicking a P2P file within FolderShare, a file on a different device would be downloaded to your computer. FolderShare was replaced by Windows Live Sync.
NOTE: The term "P2P" is also short for "peer-to-peer," which refers to Internet file sharing programs. Most P2P programs do not use the ".p2p" file extension.
Updated: December 8, 2017