There are annuities that employees in public employee retirement plans
have ((TSA, or tax sheltered annuity, generally 403(b) plans) or annuities that the annuitant purchases themselves (these are often called variable annuities).
A TSA is similar in taxation
to an inherited traditional IRA
. If funded with tax-deductible
money (pre-tax, like a 401(k) plan at your work), the payments will be taxable (since the principal or investment growth was never taxed).
If your father purchased a variable annuity product (these are called non-qualified annuities), the amount of the original investment will be returned tax free, but the growth will be taxable.
First, determine the type of annuity, and also your need for payout. If you need/want the money now, then the type of annuity will drive how much will be taxable, have taxes withheld, and get your $.
Second, determine if he was in payment status or not. That could impact the payment options (and tax deferral techniques) you could choose if you can wait for the money.
Please advise more about the annuity, and I can discuss your options in more detail.