Is it correct to say that it is disliked to perform supererogatory prayers after Asr, and that whoever enters the mosque a little before Maghrib or recites a verse of prostration after Asr or Fajr before sunrise should say "Al-Baqiyat As-Salihat" (the enduring good deeds) instead of prostrating or performing Tahiyat Al-Masjid (greeting of the mosque)? And is it true that whoever prays Asr at the beginning of its time is not permitted to perform a prostration of gratitude, or recitation, or a supererogatory prayer until sunset, or is this only a few minutes before Maghrib?

Prayer after Asr is forbidden. The time during which prayer is prohibited after Asr begins immediately upon finishing the Asr prayer, and this is the view of the majority of scholars. However, some scholars permitted prayer as long as the sun is still high.

Scholars differed regarding the permissibility of performing prayers with a specific reason (Dhawāt al-Asbāb) during times of prohibition. The more sound opinion is that it is permissible to perform them. This is the madhhab of Imam Shafi’i and the choice of Shaykh al-Islam Ibn Taymiyyah. They based their argument on the Prophet’s (peace be upon him) performance of the Sunnah of Dhuhr after Asr, his approval of someone who made up the Sunnah of Fajr after the Fajr prayer, and his command to pray Tahiyyat al-Masjid (greeting the mosque) upon entering while the Imam is delivering the sermon.

Based on this, whoever enters the mosque after Asr should pray Tahiyyat al-Masjid, because it is a prayer with a specific reason. As for sufficing with dhikr instead of Tahiyyat al-Masjid, it is not legislated.

The more sound opinion is the permissibility of performing the prostration of recitation (Sujud al-Tilawah) during times of prohibition, because it does not have the ruling of prayer. Even if it were to have the ruling of prayer, it is still considered one of the prayers with a specific reason. As for compensating for the prostration of recitation with a specific dhikr, there is no basis for it. And whoever does not prostrate should not say anything in place of the prostration, as this has not been authentically reported from the Prophet (peace be upon him).