What is the ruling on completing the recitation of the Qur’an by reciting a quarter of a hizb daily during the Fajr prayer with the intention of firming up one's memorization, and repeating this every time it is completed, along with supplication and distributing drinks and sweets after the completion?

It is legislated for the worshiper to recite what is easy for them from the Qur’an after the Fatihah. It is preferable to recite a complete surah, and it is permissible to recite a single verse, or part of a verse that has a complete meaning, or parts of surahs. It is not disliked to recite the ends or middles of surahs. It was from the guidance of the Prophet (peace be upon him) to recite a complete surah, or to divide a long surah over two rak'ahs, or to recite the beginning of a surah. It was not preserved from him that he recited the ends or middles of surahs. Some of the Salaf (pious predecessors) found it good to complete the Qur’an in prayer, especially in supererogatory prayers. It is desirable to supplicate after completing the Qur’an, and supplications are answered and mercy descends at that time.