Is it permissible to carry a paper or a notebook containing dhikr and du'a, or the book Hisn al-Muslim, during prayer (whether obligatory or supererogatory)?

If the intention is merely to carry a book or notebook during prayer, then there is no harm in that. However, if the intention is to read from it during prayer, this action does not invalidate the prayer, but it is better to avoid it as it is more conducive to khushu' (devotion) and presence of heart. This applies equally to both obligatory and supererogatory prayers. Ibn Baz said: "It is better for the supplication to be from memory, as it is closer to khushu', and there is no harm in reading from a paper."