Looks like there are 3 of the same type chip. AE must be the initials of the company that made them.
If they have something to do with the screen then I'll bet they drive the red/blue/green pixels.
To find a schematic won't be easy. It may take effort and/or money.
Now if it were my laptop, and I needed to use it...
I would try clipping away the burnt component. (I wouldn't try to unsolder it.)
I would look at the underside to look for a number.
Then the screen may work. Don't be surprised if only two colors light.
The burnt component is not necessarily the root cause. There may be another bad component which ruined the one in the photo. Other components could be bad as well.
I should state a disclaimer: it's conceivable that removing the chip could cause circuit malfunctions elsewhere. I'm only saying what I would do if it were mine. The laptop won't work until someone fixes it, and I would have to pay someone money to fix it.
Can you attach an oscilloscope to read voltages? You may get an idea what the chips do.
And they only have 5 pins. Most likely the 2 large pins go to the power supply. It may be possible to solder in a new one.
Probably a common chip. Perhaps many screens use the same type device.
Find out exactly what technology your screen is. A generic schematic may give a generic name for the burned component.