What happens if I don't enter my dependents social security number??

[SteamTrain]

Then

1)  you would get no Child tax credits, nor any other special deductions or credits that might be available for that dependent.

2) You would not be able to e-file that tax return (neither Fed not state).with that dependent on it.

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IF you are looking for the SSN, then file an extension and get hold of it in the next few months, and file the final tax return including the dependent and SSN  before October.