This appears to be a recovery scam. Someone tells you that they can recover your funds if you pay them first. So, you pay them up-front. The problem? It’s impossible for anyone to recover your funds. You have now lost your funds, and, in addition, you have been scammed.
If you send your SOL to an incorrect Solana address – and you don’t know the owner of the private key that generated that address – then your funds are irretrievably gone.
To state this a different way: there is no way to take a public address and figure out which private key generated that address.
This inability to derive the private key from the public address is actually a feature – it wouldn’t be secure to share a public address if you could figure out which private key created that address. Because then you could simply steal any private key.
There are a couple of scenarios where you send your funds to the wrong address and those funds may be recoverable:
You know the person / company that you sent the funds to – you just didn’t mean to send the funds to them. (Perhaps you previously sent them funds, and their address was still in your copy/paste buffer). Solution: contact the person or company and ask them to return the funds.
You were trying to send SOL from one wallet (let’s say Coinbase.com) to your own non-custodial wallet. But you accidentally sent your SOL to an Ethereum (or other blockchain) address generated by your own non-custodial wallet. This is often called a cross-chain transaction, and these transactions can be recovered, because you control the private key that generated the address.
If you sent SOL to an Ethereum address controlled by a custodial wallet (again, let’s use Coinbase.com as an example). Coinbase can choose to recover those funds for you – although many companies are hesitant to do so. It is possible though, so it’s worth reaching out to the company.