The High Deductible premium that is referred to on the Georgia return is a High Deductible Health Plan as defined under Section 223 of the Tax Code. This is the health policy that goes with an HSA (usually).
Section 223 does not include Medicare supplement plans as HDHPs. See the definition of an HDHP at 26 USC § 223(c)(2)(A).
Therefore, you cannot use the premiums for a Medicare supplement plan as an adjustment on the Georgia return.
Georgia says:
"An amount equal to 100 percent of the premium paid by the taxpayer during the taxable year for high deductible health plans as defined by Section 223 of the Internal Revenue Code. The amount may only be deducted to the extent the deduction has not been included in federal adjusted income and the expenses have not been provided from a health reimbursement arrangement and have not been included in itemized deductions." (page 15, item 19, of the Georgia 2019 Instructions).
[Edited 3/10/2020 4:55 pm CDT - updated for 2019]
