Not good

If your child was claimed as a dependent by someone else, and you tried to file your taxes.  You will get a REJECTION notice that will state that as the reason. 

You already know who claimed the child.  if you want to challenge the determination,

• You should file a tax return by mail claiming the child as your own dependent.
• The IRS will then contact both you and the person that claimed the child. 
• You will be required to answer some questions and the IRS will decide who should get your exemption.  
• Your taxes will be adjusted accordingly.

If you both lived with the child all year, the spouse with the highest income has first rights.

Another  problem is that you probably should be  filing a joint return. 

MFJ vs MFS

https://ttlc.intuit.com/community/married/help/is-it-better-for-a-married-couple-to-file-jointly-or-separately/00/25590

If you choose married filing separately as your filing status, the following special rules apply. Because of these special rules, you will usually pay more tax on a separate return than if you used another filing status that you qualify for.

1. Your tax rate generally will be higher than it would be on a joint return.
2. Your exemption amount for figuring the alternative minimum tax will be half that allowed to a joint return filer.
3. You cannot take the credit for child and dependent care expenses in most cases, and the amount that you can exclude from income under an employer's dependent care assistance program is limited to $2,500 (instead of $5,000 if you filed a joint return). For more information about these expenses, the credit, and the exclusion see Pub 17, Chapter 32.
4. You cannot take the earned income credit.
5. You cannot take the exclusion or credit for adoption expenses in most cases.
6. You cannot take the education credits (the American Opportunity credit and the lifetime learning credit), the deduction for student loan interest, or the tuition and fees deduction.
7. You cannot exclude any interest income from qualified U.S. savings bonds that you used for higher education expenses.
8. If you lived with your spouse at any time during the tax year:
a. You cannot claim the credit for the elderly or the disabled,
b. You will have to include in income more (up to 85%) of any social security or equivalent railroad retirement benefits you received, and
c. You cannot convert amounts from a traditional IRA into a Roth IRA.
9. The following deductions and credits are reduced at income levels that are half those for a joint return:
a. The child tax credit,
b. The retirement savings contributions credit,
c. Itemized deductions, and
d. The deduction for personal exemptions.
10. Your capital loss deduction limit is $1,500 (instead of $3,000 if you filed a joint return).
11. If your spouse itemizes deductions, you cannot claim the standard deduction. If you can claim the standard deduction, your basic standard deduction is half the amount allowed on a joint return.

You may not be able to deduct all or part of your contributions to a traditional IRA if you or your spouse were covered by an employee retirement plan at work during the year. Your deduction is reduced or eliminated if your income is more than a certain amount. This amount is much lower for married individuals who file separately and lived together at any time during the year.

If you actively participated in a passive rental real estate activity that produced a loss, you generally can deduct the loss from your non-passive income, up to $25,000. This is called a special allowance. However, married persons filing separate returns who lived together at any time during the year cannot claim this special allowance. Married persons filing separate returns who lived apart at all times during the year are each allowed a $12,500 maximum special allowance for losses from passive real estate activities.

If you live in Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington or Wisconsin and file separately, your income may be considered separate income or community income for income tax purposes. See Pub 555 Community Property - http://www.irs.gov/pub/irs-pdf/p555.pdf The states of Tennessee and South Dakota have passed elective Community

Property Laws.