What is the ruling on fasting Saturday if the National Council declared that the beginning of Ramadan was Friday, and the official announcement was on Saturday, knowing that the Council's news was not known until after breaking the fast on Friday? Is it obligatory to make up for this day?

What is religiously considered for proving the start of Ramadan is sighting (the moon) or completing the count, based on the Prophet's (PBUH) saying: "Fast when you see it (the new moon) and break your fast when you see it. If it is obscured from you, then complete thirty days of Sha'ban." So, if the authority announced that Friday is the first of Ramadan based on a legitimate sighting, then you must abstain from eating for the rest of Friday and make up that day, as you did not do so. However, if the authority was not based on a legitimate sighting, then you are not required to make up the day.