Is it permissible to make up for Qiyam al-Layl daily due to a medication that causes sleep for six consecutive hours and prevents Qiyam al-Layl in the summer, and does this apply to Ramadan, or can the Duha prayer be extended as an alternative?

If illness prevents one from performing Qiyam al-Layl (night prayer), Allah Almighty will hopefully record for you the reward of performing it for that duration, based on the hadith: "If a servant falls ill or travels, what he used to do when he was healthy and at home will be recorded for him."

If the night prayer is missed due to sleep, it is permissible to make it up during the day, based on the hadith: "Whoever sleeps past his hizb (portion of the Qur'an) or part of it, and then recites it between the Fajr prayer and the Dhuhr prayer, it will be recorded for him as if he had recited it during the night." And from Aisha: "When the Messenger of Allah, peace and blessings be upon him, missed the night prayer due to pain or other reasons, he would pray twelve rak'ahs during the day."

As for the Tarawih prayer, there is no obligation to make it up, because it is a supererogatory prayer. However, if one prays during the day whatever is easy for him, it would be better.