Search on the left side plugin

Hello.

Is there a search button plugin that has this features.

– it will stay in the page/screen even when you are scrolling down and up.
– it will only show up in product page only.

I set up an e-commerce site but I only want that search button to appear in the product page.

I can see some social icons that stays in the page/screen even when you are scrolling up and down. I also want that functionality. I don’t know what do you called that function.

If there is no such plugin, is there a way I can achieve that function by modifying the theme?

Thanks in advance. Help is greatly appreciated.

Gerandy