Tatediem marks indirect objects - these can only be humans, btw - by a specific set of prefixes (that in part are 'subsumed' in the object slot, generally prefixing themselves to the object prefix with some level of assimilation).
1 2 3 masc fem masc fem masc fem sg -heŋ- -heŋ- -win- -wir- -ŋme- -har- dual -hami- -himi- -sin- -tir- -ŋra- -ŋar- pl -hew- -hig- -cin- -cin- -ŋim- -lar-
Which, by the way, reminds me that I have not yet given the personal pronouns! Here, feminines to the right, masculines to the left:
1 2 subj obj subj obj sg -ke-, -ke- -her-, -hec- -gi-, -gi- -wir-, -ŋwiŋ- dl -am-, -im- -kiim-, -kaam- -di-, -tin- -sir-, -sin- pl -eg-, -ic- -xec-, -ki- -gi-, -gi- -cir-, -cir-
As for expressing possession, the object prefixes can be affixed between the gender prefix and the root of a noun. However, many dialects have opted for marking an empty verb-like particle in the vicinity with the gender of the possessed noun (as subject), and the dative prefix (or the object prefix for dative-less nouns) as the object. The verb is -gìan-, a verb that in some dialects also can serve as copula. It lacks all other markings except subject and object.
Conversely, some dialects use -páhí-, 'possess', and have a somewhat different structure - the possessor as possessor, and the possessee as subject. If the possessor has a dative marker, the possessee is marked with that prefix in the subject slot, whereas if the possessor is of some other gender, the possessor has a subject-like marking and the possessum has an object marking.
ye-ŋəbs = the dog
ye-her-ŋəbs = my dog
ye-kiim-ŋəbs = the dog belonging to the two of us
ye-ŋim-ŋəbs - their dog
(assimilation often hits: yeki:ŋebs/yeki:mbs, yeŋiŋəbs/yeŋ:ibs)
(ye-)ŋəbs ye-heŋ-(g)ìan = a/the dog that belongs to me (assimilated as yeŋəbs yeŋ:ì:n)
(ye-)ŋebs heŋ-ye-páhí = a/the dog that I own (assimilates to yeŋəbs heypáí)
(ye-)ŋebs ku-l-páhí = the dog that belongs to neut1 noun
Sometimes, the prefix relating to the possessum is omitted from -(g)ìan or páhí, if it is definite: