There is no harm in making supplication during the prayer, at its beginning, middle, and end, whether in the obligatory prayer or in others.
حدثنا القعنبي
لا بأس بالدعاء في الصلاة في أوله وأوسطه وفي آخره في الفريضة وغيرها
No references are available.
[Its chain is sahih.] It is in Muwatta (Yahya) 1/218, abridged.