Part number of a connector in an Asus laptop
Look for 6 pins FPC/FFC connector and 6 contacts FFC/FPC cable (eBay, Aliexpress...) and try to find a connector that looks like the one you have burned.

You must first measure the contact pitch. It can be 0.5mm, 0.63mm, 1mm, 1.27mm, ...

You could repair it with a soldering iron and good eyes, but it must have, obviously, a very fine tip.
Maybe you should practice a bit soldering before hacking the laptop and, of course, disconnect the laptop battery.