In this section the following words have the meanings indicated. “Federal adjusted gross income”, “fiduciary”, “resident”, and “taxable year” have the meanings stated in § 10–101 of the Tax – General Article. “Qualified child” and “taxpayer” have the meanings stated in § 10–751 of the Tax – General Article. A county may provide, by law, for a grant for each qualified child of a taxpayer if: the taxpayer has federal adjusted gross income lower than the threshold amount of $15,000; and the taxpayer and each qualified child are residents, other than fiduciaries, who on the last day of the taxable year are: domiciled in that county; or maintain a principal residence or place of abode in that county. The amount of a grant allowed under this section shall be reduced by 10% for each $1,000, or fraction thereof, by which the taxpayer’s federal adjusted gross income exceeds the threshold amount, except that the reduction cannot reduce the grant below zero. A county may provide, by law, for: the amount of the grant under subsection (b) of this section; and any other provision necessary to carry out the grant under this section.