Person owes me like $4.5K cash and like 4BTC. Can I sue for the btc claiming it as my personal property or something?
Of course you can. It's the same like with fiat money that someone owes you. But because of that it is the same with you having to proof that he owes you that money. Can you show a contract or something? That's always better than a spoken contract. Since when he claims you never had that deal then you will have no success at court.