sound like your derailleur hanger is bent.

I flip the bike upside down, then position the tension cage on the derailleur at a vertical position... then, look at how it aligns with the front sprockets. It should vertically align with them.

If, after you get the cage aligned, the derailleur limit screws will need set again.

it is also possible for the der. hanger to get TWISTED out of alignment to the bike's center line... shift the chain onto the smallest sprockets, then note how the cage aligns to the chain line... correct as needed, then once again check how the der. shifts, and adjust if needed.

NOW, once all that is ok, test ride the bike, and make sure to put it into the highest gear, at a medium speed... pedal as hard as you can... if it still skips, you may have worn sprockets, OR a bad freewheel or free hub ratchet!

And CHAINS don't " STRETCH" under normal conditions... they WEAR, at the pin to roller interface, and at the roller to tooth interface.... just sayin'...

and a bent/sticking chain link or two will also cause a "skip"... pedal the bike, and watch for the der. cage to twitch every time the tight link passes through the cage/rear sprockets.. this is more typical with rusty chains, or poorly installed chains.