The effect of the reaction atmosphere(reducing/oxidizing) on the band gap of the prepared powder depends on many factors;
Thermal stability, thermal literature, Porosity, materials structure[amorphous, poly crystalline or crystalline] materials type [organic or inorganic], preparing method,
The all mentioned parameters affect the structural properties of the material and may increase or decrease the band gap depending if theses factors increase or decrease
You should specify somewhat more. However, at a first glance I would suggest two main categories of GAP modification due to oxidation or reduction during powder synthesis, mainly nanopowders.
A first category relates to the chemical surface modification caused by a rich oxidizing environment, that may lead to the formation of an oxide shell encapsulating a non-oxide semiconductive core which is reduced in size if compared to the pwder produced or treated in a reducing environment. When working with very small nanoparticles this may translate into a larger GAP connected to quantum size and quantum confinement effects.
The second category involves the formation of defect states (or their electrical inhibition too) in the nanopaticle powder, or more generally the the more or less effective defect inclusion in the whole particle.body. In such cases bulk powder material is the same wether reducing or oxiding environment is applied, we should more correcly speak of possible defect states or narrow bands INSIDE the material GAP. In other words, the GAP is not modified as a valence-conduction band edges separation. Instead, electrically active defect staes inside it may cause an "appearent GAP narrowing.