During the last three decades, non-standard statistics for indistinguishable quantum particles has attracted broad attentions and research interests from many institutions. Among these new types of statistics, the q-deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems... In this paper, we construct a q-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed q-deformed BCS theory. Some interesting features of this q-deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose-Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the q-induced ``Bose-Fermi'' crossover. Conversely, a weak sign of the ``Fermi-Bose'' crossover is also found in the ordinary weak fermionic regime. (read more)