مَرَرْتُ بِالْعَصَا وَغُلَامِي: I passed by the stick and my servant.
وَ: conjunction.
غُلَامِي: conjunct of the genitive noun الْعَصَا; therefore genitive too, with an estimated kasra on mīm, whose position already carries the kasra required before possessive yāʾ.
غُلَامِ: muḍāf; ي: muḍāf ilayh.
The preposition appears only once, but the second noun inherits the genitive case through coordination.