غُلَامٌ has tanwīn, but غُلَامِي does not: the mudāf does not retain tanwīn.
The kasrah before the possessive yāʾ accommodates that attachment. It does not prove that the whole noun must be in the genitive case.
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Why Tanwīn Disappears
Iḍāfah to Yāʾ al-Mutakallim and the Six Nouns
غُلَامٌ has tanwīn, but غُلَامِي does not: the mudāf does not retain tanwīn.
The kasrah before the possessive yāʾ accommodates that attachment. It does not prove that the whole noun must be in the genitive case.