Paser I was the Viceroy of Kush during the reigns of Ay and likely Horemheb.
Reisner mentions that the only datable inscriptions for Paser belong to the reign of Ay.
Hence it's possible that Paser I served during the reigns of Ay, Horemheb (and maybe even Ramesses I?).
[1] Paser was the son of the Viceroy Amenhotep called Huy, who served during the reign of Tutankhamun.
[2] Paser's titles include: Overseer of the Gold Lands of Amun, King's Son of Kush, overseer of the Southern Lands.