There is no such match. Parents can gift money to the child in the form of a Roth IRA contribution (provided the child has sufficient compensation to support the contribution), but for tax purposes this is still a contribution of the child, subject to the child's contribution limit, no matter who makes the deposit.
Note that the money the child received must be reported on the child's tax return as income from self-employment. Assuming no other compensation, the maximum that the child can contribute for 2022 is the net earnings from self-employment or $6,000, whichever is less. Net earnings from self-employment are net profit on Schedule C minus the deductible portion of self-employment taxes. For $4,000 of self-employment net profit that would mean a maximum Roth IRA contribution of $4,000 - $283 = $3,717. If all of the child's net profit has been contributed, there is already an excess contribution to this child's Roth IRA.
