If the other parent claimed your child and received the stimulus for him, you might be able to get it when you file your 2020 return next year in 2021 if you claim the child as your dependent on that return.
You did not really explain fully what your tax situation is--do you and the child's father live together? And when you refer to "last year" did you mean 2018 or 2019?
There were a number of people who did not receive the $500 stimulus money for their children under the age of 16, for various reasons. The stimulus checks were an advance on a credit that can be claimed on 2020 returns, so those who did not receive it yet can get it next year.
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