ənta ʕəndək bəlɣ-at-ək w ana ʕəndi bəlɣ-at-i انتا عندك بلغاتك وانا عندي بلغاتيand for xədm-a خدماتك "work", completely unprompted:
"You have your flip-flops and I have my flip-flops."
kəmmli xədm-at-ək كمّلي خدماتكwhich his older brother actually corrected to kəmmli xəddəm-t-ək كمّلي خدّمتك.
"Finish your work."
Adults' speech furnishes one plausible model for this strategy - not in nouns but in participles. The active feminine participle takes direct object pronoun suffixes, identical to the genitive ones except in the 1st person singular. In such forms, -ət becomes -at before a vowel, rather than dropping the ə: šayf-a شايفة "having seen (f.)", šayf-at-u شايفاتهُ "having seen him (f. subject)". But its extension to nouns is something quite new; neither their parents nor their elder brother nor any adult I've met use such forms.
Most probably, the next time I go to Dellys I'll find these two children using the normal forms and denying they ever spoke this way. Even now, they already use the normal form for body parts which almost always occur possessed: rəqb-a رقبة "neck" becomes rəqqəb-t-i رقّبتي "my neck". But what if this innovation instead spreads among their peers? Most likely it won't: there seems to be little evidence for children initiating language change, notwithstanding the idea's widespread adoption by generative historical linguists, and adults' innovations are much more likely to be maintained or copied (cf. Luraghi 2013, Foulkes and Vihman fc; for a potential counterexample, see Moyna 2009). For that very reason, however, it will be worth keeping an eye on them; potential counterexamples are always interesting.