Catalyzes the formation of sulfite from adenosine 5'-phosphosulfate (APS) using thioredoxin as an electron donor. [thioredoxin]-disulfide + AMP + 2 H(+) + sulfite = [thioredoxin]-dithiol + adenosine 5'-phosphosulfate Binds 1 [4Fe-4S] cluster per subunit. Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate. Up-regulated by sulfur starvation and repressed by cysteine. Also induced by O-acetyl-L-serine (OAS), a direct precursor of cysteine, maybe via inactivation of a putative transcriptional repressor of the cysH operon whose activity is controlled by the intracellular levels of OAS. Belongs to the PAPS reductase family. CysH subfamily.