You will really need to be more specific.
When considering unclaimed funds (such as from a state's unclaimed property office) the money is taxed according to what it was and how it would have been taxed.
For example, suppose your father had a life insurance policy against your mother, and forgot to file the claim when she died. Then your father died and the life insurance company couldn't find the policyholder so the money went to the state and you found it. Because life insurance death benefits are not taxable, the "found" money is not taxable to you.
On the other hand, suppose your father died and your mother moved in with family, and forgot to claim her survivor's benefit from your father's pension, and those funds went unclaimed. Because the pension benefit would have been taxable to your mother, it is taxable to you now that you have found it.
Or lastly, suppose your father owned stock in XYZ company. He purchased the stock for $1000. When he died and the broker couldn't find him, they sold the stock for $3000 and put the money in the state's unclaimed funds account. Since that represents a $2000 capital gain, that's what's taxable to you (and the tax on capital gains is less than the tax on other income). Or, if the stock was purchased for $4000, then you are receiving the money at a loss and the $3000 from the state is not taxable because there is no gain. But if you get audited and can't prove the price your father paid, the IRS can determine the entire $3000 is a capital gain to you.
If audited, the IRS has the right to assume all money is taxable unless you can prove otherwise, so a thorough investigation and documentation of the funds may be important to you in the future.
For other kinds of property, we really need more details.
