Yes, if you are claimed as a dependent, then you may have to claim the distribution as income.
I am assuming that you are the beneficiary on the ESA and that your parents are claiming an education credit.
Withdrawals from Coverdell ESAs generally are tax-free to the extent that the withdrawal is not more than the beneficiary's qualified education expenses.
If your parents are taking the education expenses on their return, you need to figure out if any is left to offset your ESA distribution.
Here is an example of how this is calculated from IRS Publication 970:
"Derek Green had $5,800 of qualified higher education expenses for 2021, his first year in college. He paid his college expenses from the following sources.
Partial tuition scholarship (tax free)$1,500
Coverdell ESA distribution1,000
Gift from parents2,100
Earnings from part-time job1,200
Of his $5,800 of qualified higher education expenses, $4,000 was tuition and related expenses that also qualified for an American opportunity credit. Derek's parents claimed a $2,500 American opportunity credit (based on $4,000 expenses) on their tax return.
Before Derek can determine the taxable portion of his Coverdell ESA distribution, he must reduce his total qualified higher education expenses.
Total qualified higher education expenses $5,800
Minus: Tax-free educational assistance − 1,500
Minus: Expenses taken into account in
figuring American opportunity credit − 4,000
Equals: Adjusted qualified higher education
expenses (AQHEE) $ 300" -IRS
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