Who holds the private key?

[Johnnydanger]

Who holds the keys ?

The last wallet who had the currency? The company that sold the bitcoin,etc...?

I purchased some bitcoin currency, it went to another site for a wallet, it was then transferred to a 3rd site to exchange then transferred to the wrong address(actually right address but wrong currency). Who in this equation(if any) would have the private keys to these coins?

Thanks.

[HCP]

It depends on the type of address and the currencies involved...

Theoretically, whomever owns the address that the coins were sent to, should have the keys... But it's possible, given that you've stated that an incorrect currency address was used, that no one currently has the private keys for it...

The reason the currencies involved is important, is that if they're "similar" like BTC and BCH, the private keys from BTC will generate the same address on BCH and vice versa...

However, in the situation where coins are not "similar", it is possible that due to differences in the algorithms for how private keys are converted to public keys/addresses... That no one (or some random party) is in control of the private keys that the coins are now associated with...

What currencies were involved in this incident?

[Johnnydanger]

It depends on the type of address and the currencies involved...

Theoretically, whomever owns the address that the coins were sent to, should have the keys... But it's possible, given that you've stated that an incorrect currency address was used, that no one currently has the private keys for it...

The reason the currencies involved is important, is that if they're "similar" like BTC and BCH, the private keys from BTC will generate the same address on BCH and vice versa...

However, in the situation where coins are not "similar", it is possible that due to differences in the algorithms for how private keys are converted to public keys/addresses... That no one (or some random party) is in control of the private keys that the coins are now associated with...

What currencies were involved in this incident?

The currencies involved were Bitcoin and Bitcoin cash. I think they have the same keys?

I actually posted the correct address for my bitcoin wallet however I did not realize I was transferring Bitcoin Cash not regular bitcoin.

Is there anyway to tell if some person/organization has claimed the coins or if they are sitting unclaimed? 

Would some of the wallets/websites involved have the private keys if they could agree to help?

Thanks.

[TryNinja]

The currencies involved were Bitcoin and Bitcoin cash. I think they have the same keys?

They do because they share the same address/private key space. An address and its private key are the same in both chains - even if the balances will be different.

Is there anyway to tell if some person/organization has claimed the coins or if they are sitting unclaimed? 

Yes. You can search the address in a BTC explorer to see if the address still has BTC and in a BCH explorer to see if they still have the BCH.

Bitcoin Explorer: https://blockchain.info/
Bitcoin Cash Explorer: http://blockdozer.com/insight/

Would some of the wallets/websites involved have the private keys if they could agree to help?

Maybe. I have seen a lot of services not wanting to help a user recover its BCH sent to a BTC address. Others, will help you if you provide enought information through their support. So, you need to ask them if they are willing to help you.

[HCP]

Would some of the wallets/websites involved have the private keys if they could agree to help?

What wallet has the address that you used? Was it a desktop wallet like Electrum or BitcoinCore or was it a web wallet?

In either case, if that wallet allows you to export private keys (or has a 12 word backup phrase)... Chances are good that YOU have the private key and can simply import that key into a BCH wallet and get access to your misplaced BCH

[HCP]

It's very possible... do a Google search for "accidentally sent LTC to SegWit address"

There is a reason they put all the warnings on deposit address screens on the exchanges... There are a number of coins that use similar address algorithms and you can end up creating a so-called "cross chain" transaction...

Which, essentially just means that you sent funds to a valid, but unintended address. Sometimes you can recover the funds, sometimes you cannot. It depends on the currencies involved, the algorithms for converting private key to public address and who "controls" the private key.

In this case, I believe the OP is out of luck as, while it was a BCH to BTC address situation... He doesn't have the private keys as it was an exchange based deposit address and they seem to have a "we don't help for incorrect deposits" policy

Note: We will not refund an incorrect withdrawal/ Deposit. This deposit address is for BitCoin (BTC) only.