How to restore some percentage of backup file?
You probably have an option of:


Create several filegroups and data files in these filegroups
Move some part of your data to new files using rebuild index command
When restoring your database from a backup specify remote location for some data files, and the other files restore locally.


Some useful links to begin with:


Move an Existing Index to a Different Filegroup (Microsoft Docs)
SQL Server Can Run Databases from Network Shares &amp; NAS by Brent Ozar