More detail needed. Is this for tax year 2019. Did you both already e-file and were you accepted. It would be highly unusual for him to get a letter in the mail already for 2019.
"My ex husband and I claimed the same child". That's actually allowed, to an extent.
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner. The IRS goes by physical custody, not legal custody
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child , even when the custodial parent has released the exemption to him.
"He got a letter in the mail today stating something is wrong and it needs to be change." If this was for last year, you may be getting the same letter. The two of you have to figure out what that "something" is. Then one (or maybe both) of you will have to file an amended taxreturn
