last year during Ramadan I did a big mistake by trying to call adhan close to iftar time(like a joke)at home not in a masjid and unfortunately my mother and uncle both broke their fast by eating little before I informed them ,sincerely I regreted it but, I want to know whether I am to fast 60-60 for both if yes can I live the other 60 till after the next ramadhan? The reason I delayed asking was that I wanted a reliable and authentic source though I ask one great imam in a lecture but he responded to the question the day I didnt attend the lectures and neither of my colleagues heard the response.May Allah(SWT) continue help you with this great gigantic task!
Praise be to Allah
You did wrong by imitating the voice of the mu'adhdhin at the time when the people were waiting for the adhaan in order to break the fast; you should have respected the importance of accuracy in timing for those who were fasting.
If you did that with no intention of disrespect towards the adhaan or the fast, and with no intention of deceiving those who were fasting, then you do not have to do anything. But you do have to learn a lesson from that, which is how to act appropriately in different situations, and that there is a time for seriousness, at which it is not appropriate to engage in any kind of play or fooling about.
But if you did that to deceive them, so that they would break their fast (at the wrong time), then you have to repent, seek forgiveness for what you did and regret your actions. However, you do not have to offer expiation, whether that is by fasting two consecutive months or otherwise.
With regard to your mother and maternal aunt, there is no sin on them, because they broke the fast thinking that the time for Maghrib had begun.
But do they have to make up that day or not? There is a difference of scholarly opinion concerning that; the majority are of the view that that day must be made up.
However some of the scholars favoured the view that it does not have to be made up and the basic principle is that the duty has been fulfilled and there is nothing in Islam to suggest that it must be made up in such cases, even though something similar happened at the time of the Prophet (blessings and peace of Allah be upon him).
This is the view favoured by Shaykh al-Islam Ibn Taymiyah, and is also the view of Shaykh Ibn Uthaymeen (may Allah have mercy on him).
However, if a person wants to be on the safe side with regard to his worship and to avoid an area of considerable scholarly difference of opinion, and he makes up that day, this is better, especially as making up one day is something easy, and is not usually difficult for people.
Shaykh Ibn Baaz (may Allah have mercy on him) said:
If a person drinks, thinking that the sun has set, then the sun appears, then he should make up that day according to the view that is regarded as correct by the majority of scholars, and this is more on the safe side. Some of the scholars do not think that it has to be made up, because he is excused as he did not do that deliberately. However, the view that is more likely to be correct is that it should be made up.
End quote from Fataawa Noor ala ad-Darb by Ibn Baaz (Shuwayir compilation, 16/267
Please see also the answers to questions no. 38543 and 66155
And Allah knows best.