Do you need to pay tax on your father 401 K inheritance?

Yes if you are the beneficiary of your fathers 401K.

The taxable amount of the distributions will be taxed to you in the same way that they were taxed to your father.

Inherited pension or IRA. If you inherited a pension or an individual retirement arrangement (IRA), you may have to include part of the inherited amount in your income. See Survivors and Beneficiaries in Publication 575, if you inherited a pension. See What If You Inherit an IRA?

Expected inheritance. If you sell an interest in an expected inheritance from a living person, include the entire amount you receive in gross income on Form 1040, line 21.

Bequest for services. If you receive cash or other property as a bequest for services you performed while the decedent was alive, the value is taxable compensation.

See the information at the link provided below for some practical, easy-to-read information about inheriting an IRA.