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.
Xiong, "onUN"="his", genitive case for possessive pronoun third person singular, and "cüzdanIM"="my wallet", possessive case suffix, first person singular, are antinomic. It is either "onun cüzdanı"="his wallet" or "(benim) cüzdanım onda"=he has my wallet = my wallet is on him (literal translation). And "cüzdan-ım-sı" is impossible, because "ım" possessive suffix first person singular and "sı", possessive suffix third person singular can't work together as AGreatUserName explains in his comment.
MartenDKgy, in him!? Where in his body? In his stomach? In his leg? Do you remember locative skill? Think of those sentences: "çay onlarda"="they have the tea", "Elmalar sende"="you have the apples", "Ördek bende"= i have the duck", etc.. and now: "Benim cüzdanım onda"="he has the wallet of mine", literaly.