Is it permissible for scholars to issue fatwas based on ijtihad without relying on a hadith or a Qur'anic verse, and what is the evidence for that?

There is no room for ijtihad (independent reasoning) when there is a clear, explicit religious text that leaves no room for interpretation, or when there is an explicit consensus (ijma'). However, in the absence of a text, or if a text has more than one meaning, scholars exert ijtihad to arrive at the correct conclusion. Ijtihad is the work of a mujtahid (one who performs ijtihad) and his consideration of religious evidence to deduce a specific ruling, and it is not evidence in itself. It is not accessible to everyone, but only to those who know the principles and rules of inference, and its conditions are explained in the books of Usul al-Fiqh (principles of Islamic jurisprudence).