Is it possible to fix this? If so, then how?

I bought a used Iphone 4 and updated and reset it through itunes, but whenever I put in my icloud account it says to put in the original icloud account, so is there anyway to remove it?

Try the store

No. You probably bought a stolen phone.
There's no way to bypass iCloud lock. You can ask the seller if they can remove the iPhone from their iCloud account, but if they don't know how, then you are out of luck.