In my house I have an al-Fajr clock that gives the adhaan at the times of prayer. There are no mosques in the city in which we are living. Is it prescribed to respond to the adhaan on the clock or not?.
It is not prescribed to respond to the recorded adhaan, because it is not a real adhaan, i.e., it is not done by the muezzin at the time; rather it is a recording of a previous adhaan.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about the adhaan on the radio or television: should one respond to it? He replied:
With regard to this adhaan, one of two things must be the case:
(i) It is on the air, i.e., the adhaan is being given at the time of prayer by the muezzin. In this case it should be responded to, because of the general meaning of the command of the Prophet (blessings and peace of Allah be upon him): “When you hear the muezzin, say what the muezzin says.” But the fuqaha’ (may Allah have mercy on them) said: If he has offered the prayer for which the call is being given, he does not have to respond.
(ii) The adhaan is recorded and is not an adhaan being given at the time; in this case it should not be responded to, because it is not a real adhaan, i.e., the man is not giving it at the time it is commanded to give it; rather it is an audio recording of a previous adhaan.
End quote from Majmoo‘ Fataawa al-Shaykh Ibn ‘Uthaymeen, 12/196
What is prescribed is for you to give the adhaan in your house, so that you may attain the reward of this great ritual, because of the report narrated by al-Bukhaari (609) from ‘Abd al-Rahmaan ibn ‘Abd-Allah ibn ‘Abd al-Rahmaan ibn Abi Sa‘sa‘ah al-Ansaari from his father, who told him that Abu Sa‘eed al-Khudri said to him: “I see that you like sheep and the wilderness. When you are with your sheep in your wilderness, and you recite the Adhaan for your prayers, raise your voice, for no jinn or man or anything within the voice range of the muezzin hears the call, but will bear witness for him on the Day of Resurrection.” Abu Sa’eed said: I heard this from the Messenger of Allaah (peace and blessings of Allaah be upon him).
It is also prescribed for you to respond to the real-time adhaan that is transmitted live on the radio or television, as stated above.
And Allah knows best.