If the adhan is called while performing a missed (qada) prayer, can one continue with the qada prayer?

The calling of the adhan for any prayer time while performing a missed (qada) prayer does not affect the validity of the qada prayer being performed. There is no specific time required for making up missed prayers; qada prayers can be performed at any time except during the times of karahah (disliked times). The times when prayer is not allowed are specified in the hadith narrated by Uqbah ibn Amir: “The Messenger of Allah (peace be upon him) forbade us from performing prayer or burying our dead during three times: from the rising of the sun until it has fully risen (the length of a spear or two), when the sun is at its zenith until it moves westward, and from when the sun begins to set until it has fully set.” (Muslim, Salat al-Musafirin, 293 [831]; see also Abu Dawud, Tatawwu‘, 298 [1277]; Janaiz, 55 [3192])

During the time of karahah before sunset, only the obligatory (fard) Asr prayer of that day may be performed. However, it is disliked (makruh) to delay the Asr prayer until this time without a valid excuse.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu