This is OP. Thank you guys! As some responded I never thought it's the law. That's why we ask questions to be better informed.
Happy Holidays and Happy New Year 2021.

No, a bonus is completely voluntary.

Though if you haven’t worked for a family for long, you likely will not get very much.

Hopefully you still have a Merry Christmas tomorrow OP!

Of course it's not a law or mandatory in any way. And why are you comparing families anyway? Some families give gift cards, some don't. Some give a prorated amount (it sounds like yours did), others give 1 week, others give two weeks. It's a bonus, a GIFT.

In the nanny world bonuses are almost like tipping. It's sort of understood but not mandatory (unless written into the contract which in this type of relationship is hard to enforce anyway). It should not be considered the defining provision of the nanny/family relationship but more of a mutual understanding between the two parties and their abilities to provide such benefits). (( I'll give you five dollars if you can guess my geographical location and the principal occupation of most of my 'clients').

Nanny here, Op it is not mandatory by any means. It's simply and purely voluntary. Don't take it personally. Some families are just not that generous even if they have the money and you are a Mary poppy nanny.
My current employer last year gave me a "meh" bonus compare with my former nanny families. I felt disappointed, but I did not make a deal of it.
This year my bonus (with the same family) was three times more than last year!
They said it was a tough year and appreciated how easier I made their lives during the pandemic. Also, I did not have time off during quarantine as other nannies.

Why would you think a bonus is “required by law?”

Of course it's not a requirement by law to give a bonus. A bonus is extra, totally voluntary.

I only give a week's bonus to a nanny who has worked for a full year.

It’s not a requirement. It’s also not required that you go above and beyond when you don’t receive one. I’m done providing extras after not getting one. Only cooking kid meals from now on, the parents can eat crackers for dinner for all I care.

I have an important question for families and nannies. Is it a requirement or a law to give a bonus to the nanny? If yes, for a nanny who only works for few months how much do you give? I am a nanny and I'm working for a family for less than 6 months and they gave me a bonus of $200. Previously, all the families I have worked even for two months gave me the week of bonus. Therefore, I'm wondering if it's required by the law or just for the appreciation.
Thank you