What is the intention for the Night Prayer, and is there a supplication in the first rak'ah, and what is it?

For the night prayers other than Witr, the intention of a general supererogatory prayer suffices. As for Tarawih prayers, some scholars stipulate a specific intention for them, while others deem the intention of a general supererogatory prayer sufficient. Aisha, may Allah be pleased with her, stated that the Prophet, peace and blessings be upon him, would begin his prayer after rising from sleep at night with supplication.