You are correct. Your maximum HSA contribution limit is prorated by the number of months you are an eligible individual on the first of that month. Eligible individual 6 months = maximum contribution * 6 / 12 = 50% of applicable contribution limit.
There is an exception to the prorata rule for partial year eligibility, when the contributions come at the end of the year and you are an eligible individual on 12/1. This is called the "last month rule", but since you do not qualify I will not describe it in detail.
If you contributed the full applicable contribution, then you have a 50% excess contribution. That excess contribution and earnings must be returned by your tax filing deadline including extensions.
If you made pre-tax contributions by payroll deduction, the excess contributions are reported as taxable income. If you made direct contributions to the HSA account, a deduction for the excess amount is not claimed. In either case the earnings on the excess contribution are reported as taxable income.
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