I try to read a Juz a day. While doing so, thought, why not recite the Juz INSIDE prayer...so I started to hold my Quran and reciting from it during the optional prayers (Sunna Rawaatib). Is this permissible?

Yes, it is permissible to hold a Quran in your optional prayer, giving that you need to keep your movements (in opening, closing, and flipping the pages) to the minimum.

May Allah swt accept from you.