You could claim your child as a dependent if the child meets all the requirements to be your dependent. If you go through the Personal Info section of TurboTax it will ask you questions to determine whether or not you can claim your child as a dependent. But claiming your child won't make any difference in your taxes. If Social Security benefits are your only income, you do not have to pay any tax and you are not even required to file a tax return. Claiming your child cannot make your tax less than zero. You cannot claim the Earned Income Credit (EIC) or the Child Tax Credit if you have no "earned" income. Earned income is income from working. Social Security benefits are not earned income.
If tax was withheld from your Social Security benefits, you should file a tax return to get a refund of all the tax that was withheld, even though you are not required to file. But your refund will be the same whether or not you claim your child as a dependent.