"rām rasāyan tumhare pāsā" is Chaupai 32 of the Hanuman Chalisa, which Tulsidas wrote in Awadhi. It means: You hold the elixir of devotion to Rama, and you remain forever the servant of the lord of the Raghus. Read it slowly, one half at a time, and say the Awadhi aloud.
राम रसायन तुम्हरे पासा ।सदा रहो रघुपति के दासा ॥rām rasāyan tumhare pāsāsadā raho raghupati ke dāsā
You hold the elixir of devotion to Rama, and you remain forever the servant of the lord of the Raghus.
Awadhi text: Goswami Tulsidas, Gita Press reading, checked against three Gita Press printings and Rambhadracharya's Mahaviri. English meaning and word glosses: Wisdom's own, following the traditional reading, edited by Ankur Shukla.