What role does the letter у play in these sentences?

What role does the letter у play in the following sentences?

У мальчика молоко.
У мальчика нет молока.
У девочек велосипеды.
У девочек нет велосипедов.

Russian has an unusual way of expressing possession. I think it may come from Finnic or Ugric, but my historical linguistics is rusty. If you are familiar with 1950s American music you might remember
Bei mir bist du shein By me are you pretty. Yiddish (which btw is strongly influenced by Slavic)
Similarly for Russian possession
By the kid is milk. The child has milk. also The child's milk.
The girl has a bicycle. The girl's bicycle.

It is normal. There is a Russian verb иметь have, but it is rare enough (and not equivalent to the у + GENITIVE construction) that you won't need it until second year Russian at the earliest.

An addendum. ))))

у меня (есть) - I have
у меня нет - I don't have
у меня два брата - I have two brothers
У меня нет братьев - I don't have any brothers

У мальчика молоко = У мальчика (есть) молоко = The boy has milk.
У мальчика нет молока = The boy has no milk.
У девочек велосипеды = У девочек (есть) велосипеды = Girls have bikes.
У девочек нет велосипедов = Girls don't have bikes

I was surprised when I learned that for the first time, because Arabic has the same exact sentence structure for "to have".

'indi sayyara ('ind = at/by, -i = first person accusative/possessive pronoun, "me", and sayyara = car).