Is there a specific supplication for one who dies at the age of three months, and what is the reward for such children with Allah?

One who loses a young child is rewarded. There is no specific supplication for those who die at this age. A child who dies before reaching puberty is not held accountable; rather, they are under the care of Abraham (peace be upon him). Whoever endures with patience and praises Allah upon losing a child will be admitted by Allah into Paradise through the intercession of that child, and a house called "Bayt al-Hamd" (the House of Praise) will be built for them therein. As stated in authentic hadiths, young Muslim children who die are the "Dama'is of Paradise" (butterflies/dragonflies of Paradise) and will intercede for their parents.