I don’t know if there is one but many are POS and they even have burning. But not that much to say, you probably are looking for an altcoin that will get shilled to you.
Expect that you will be bombarded by a lot of random name altcoins that won’t even be close to the description that you’ve given. If you are for the POS, ETH is one IMO.

Bitcoin is the king of cryptocurrency and in a kingdom we have only one king, which means no one can be like or act like the king. This is how bitcoin is to these altcoins, since they are duplicate of bitcoin and bitcoin is decentralized while most of the altcoins are centralized making it impossible for a PoS coin to be like Pow because the two are different.

It is impossible for you to see such altcoins, so just forget about it.

I do not think there are any PoS cryptocurrencies quite like Bitcoin when it comes to havings and a limited supply.  That whole thing is tied into Bitcoin’s proof-of-work mining structure.

However, some PoS coins do cap the maximum number you can mine.  A few even try to reduce inflation in their own way, just not with the same halving reward thing as Bitcoin.  They might use different systems to increase scarcity over time.  But as far as mimicking Bitcoin’s specific economic model, I cant think of any PoS altcoins doing that so far