does the notice contain info on how to refute the finding? if there's a phone number call it to see what they say. otherwise, all you can do is file an amended return. you would have to change your original return to what the IRS found which would likely require removing the dependent. close it. then open to amend it and add the dependent back.
You should be able to handle this by replying to the notice.
After entering on 1040-X Col A the IRS-adjusted amount that reduces your refund or make you owe,
enter in Col C the amount you had in the first place.
In Explanation, state you are reinstating your dependent with their correct Social Security Number.
You must list all dependents.
The amount on Line 18 will depend on your decision whether or not to pay any amount the IRS is asking for now.
IRS processing time for 1040-X is currently about ten months.
This is exactly the reason to efile when at all possible as the incorrect SS# would have been rejected immediately and you could have fixed it and resubmitted the return within a day. Now this issue will take months to correct.