Can we make supplication during prayer, and when should we do that?
First of all, we should take the Prophet Muhammad (peace be upon him) as a role model and follow him in all his aspects of life as the best guidance is the guidance of the Prophet (peace be upon him). Supplication is a great act of worship. It is a clear sign of one’s faith. When one makes supplication to Allah whether by whispering or by heart, we affirm that Allah can hear us. We affirm that he loves and cares about us and also has the power to answer our supplication.
It was narrated that the Prophet (peace be upon him) said, “Du`aa’ (supplication) is worship” (Abu Dawud)
Abu Hurairah (May Allah be pleased with him) narrated that the Messenger of Allah (peace be upon him) said, “A slave becomes nearest to his Lord when he is in prostration. So increase supplications while prostrating.” (Muslim)
Answering this question, Dr. Muhammad Salah states that the Prophet (peace be upon him) recommended us to increase our invocation and supplication while making sujud (prostration) during prayer. Also, the Prophet (peace be upon him) used to recite certain supplications before making tasleem. Dr. Muhammad also mentions that some people may make supplications in congregation after finishing the prayer which is not prescribed. Finally, making supplications after the prayer is not part of it.
Source: Iqraa Channel.