Answers
According to the pertinent provisions of the Greek law, as recently amended with Law 4587/2018, inherited properties or properties acquired through parental donation are eligible for Golden Visa. However, in such a case, the fair-market value of the property will be taken into consideration in order to determine your eligibility for the Greek Golden Visa. Accordingly, if the fair-market value of the property is at least 250,000 euros, then you qualify for the Golden Visa.
The father can transfer the real estate with a donation to his child.
Following to recent clarification from the competent authorities on Greek immigration law provisions, third-country citizens who are adults and who fully and legally own real estate property in Greece, the minimum value of which is 250,000 euros, acquired through intestate succession, will or parental concession are eligible for Golden Visa program.
No, you aren't eligible for a Golden Visa for inherited properties.
You cannot apply for Golden Visa like that. You should buy a property with price of 250,000 euros. So only if you buy the property from your father and pay him 250,000 euros can you apply for a Golden Visa.