I sent some funds to my MEW wallet but I fat fingered the address and sent it to a different address that does not seem to exist. How do I claim that address to retrieve funds I see sitting in the block.
Unfortunately, you cannot claim that address. Those funds are lost forever.
A feature of Ethereum is that there are so many possible addresses that one cannot "choose" an address. This allows for a basically unlimited number of addresses to exist.
You can see more about addresses here.