ipod nano 7th gen just blinks on and off

The Restore is done in iTunes; it's not something that starts by itself on the iPod. If the screen is black, and iPod does not appear in iTunes (where you can select it and click the Restore button), I don't think the iPod went into Disk Mode. The iPod probably has a hardware problem that is preventing it from starting up properly, regularly or in Disk Mode.

The iPod has a "secret" diagnostic mode. You can try putting into diagnostic mode, to see if you learn anything new about the problem. This YouTube video describes how

https://www.youtube.com/watch?v=Nv2FBzRl45U

If it's less than one year from purchase date, it is under standard warranty.

Describe what iPod's screen shows when you connect it. Does it say "connected" or "do not disconnect" or give other indication of a data connection? Or does it only show battery charging symbol? Or are you actually saying it just "blinks" without showing anything on it?

Does anything happen in iTunes when you connect it? The iPod should appears as a device button on iTunes window. Here's a screenshot of my iTunes window (upper-left corner), showing iPod's device button, circled in red.

If you see that button, click it to show iPod's Summary settings screen in iTunes window.

NOTE: iTunes must be installed on your computer to use an iPod. If you have not already, you can download the latest version from here

https://www.apple.com/itunes/

Run the downloaded installer. Launch iTunes and connect iPod.

it only shows apple logo...

So, you're saying the iPod never completes its startup to show its home screen? It's stuck showing the Apple logo on the screen? What happens when you do a Reset (restart) on the iPod

Learn how to reset your iPod - Apple Support

Does it get stuck showing the Apple logo again? If iPod completes startup to show its home screen, connect it to computer running iTunes. It should work now.

If it's stuck showing the Apple logo after a Reset, try putting it into Disk Mode

How to put your iPod into disk mode - Apple Support

If it goes into Disk Mode, connect it to computer running iTunes. iTunes prompts you to do a Restore on iPod, with a message about "recovery." If the cause is data corruption on iPod (and there's no hardware problem), doing a Restore (which erases iPod and sets it to default "factory" condition) should make it work again.

So to clarify, when you say "started blinking again," that means iPod's screen is only showing the Apple logo. It does not get to the regular home screen.

If that's correct, when you put it into Disk Mode, what does the screen show?

In Disk Mode, the screen should indicate it is in Disk Mode. When you connect it to your computer, the screen should indicate it is connected. The screen should not be black or blank.

Did iPod appear in iTunes when connected (in Disk Mode)? Were you able to select iPod in iTunes, and do a Restore in it?

"Blinks"? Are you describe an iPod nano, or the little light on an iPod shuffle?