No. You can't add a second possessive suffix after a first one - it wouldn't make sense. "His my wallet"? (Also, "-sı" is only used after a vowel. If you could use this suffix at all here, it would just be -ı, but note that cüzdanımı is just the accusative form of cüzdanım.)
Turkish distinguishes between having something as one's possession and simply having something in one's possession.
Benim cüzdanım var. = I have a wallet. (Literally "My wallet exists.") This means that the wallet is mine, I am the owner, regardless of where it is.
Benim cüzdanım onda. = He has my wallet. (Literally "My wallet is at him.") We know that the wallet is mine because of the suffix -ım. He currently has it - it's not his wallet though, so we can't call it cüzdanı ... it's my wallet.