It's a modern a Hindu religious token, known as Ramatanka, sold near Hindu temples as "antiques". The oldest hat I've seen verified was from the 1950s.
It shows a Durbar scene.
Obverse: Rama standing on left, holding trident, and Lakhsmana standing on right, holding bow.
Reverse: Rama and Sita seated on Durbar platform. Attendant standing on left holds parasol above them. Kusha and Lava, the two sons of Rama and Sita, standing on right. Hanuman kneels below platform.