No, you cannot claim that amount as a personal contribution.
Even though the description for box 12 code W on your W-2 shows 'employer contribution', it also includes contributions that were made through payroll deductions from your income. These contributions were made with pre-tax money and will be automatically taken into account in the Health Savings Account (HSA) section of your return.
The input asking about any additional contributions that you made outside of your employer is referring to contributions made with after-tax money. Anything entered here would be reported as a deduction on your return. Including your payroll contributions here would be double-dipping.
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