For children, all major New York passes offer discounted versions. Generally, child prices apply to age groups between approximately 3 and 12 years (the exact age varies by pass provider). Toddlers under 3 years often don't need a pass, as many attractions are free for them.
Special discounts for seniors, students or other groups are usually not available, the passes typically only distinguish between adult and child rates. However, it's worth checking whether children are free or cheaper at individual attractions depending on their age before buying a pass for them.