Q: how to create recover partition

What Mac OS X are you using?

To start up from OS X Recovery, hold down Command (⌘)-R immediately after turning on or restarting your Mac. Release when you see the Apple logo.

More info about OS recovery partition: About OS X Recovery - Apple Support

If you want to create a bootable USB, here is a useful guide: Create a bootable installer for OS X - Apple Support

There are two methods. Back up your system first.

• Download OS X from the App Store and reinstall it. This will not harm your data, user accounts or settings. It will only reinstall OS X on top of itself and rewrite the Recovery HD. Check the App Store afterwards for any updates.
• Download OS X from the App Store, but QUIT the installer after download. Then use this utility which uses the Install OS X ????????.app file located in /Applications. The utility will ONLY rewrite the Recovery HD.