A gas turbine system comprising: a turbine combustor, comprising: one or more first fuel injectors coupled to a head end of the turbine combustor and configured to deliver a first portion of a fuel to a first axial position of a combustion section of the turbine combustor; one or more second fuel injectors coupled to the turbine combustor axially downstream of the head end, wherein the one or more second fuel injectors are configured to deliver a second portion of the fuel to a second axial position of the combustion section of the turbine combustor, the second axial position being downstream of the first axial position; an oxidant supply system configured to provide an oxidant to a head end of the combustion section of the turbine combustor; a fuel supply system configured to supply the fuel to the one or more first and second fuel injectors; a sensor configured to measure a parameter of soot and/or ammonium in an exhaust gas from the turbine combustor; and a controller configured to cause the one or more first fuel injectors to deliver the first portion of the fuel such that combustion of the fuel and oxidant at the first axial position is oxidant-rich, and to cause the one or more second fuel injectors to deliver the second portion of the fuel such that combustion of the fuel and oxidant within the overall combustion section of the turbine combustor is at a defined equivalence ratio between 0.95 and 1.05, wherein the controller is configured control the first portion of the fuel and the second portion of the fuel to reduce a level of soot produced in the combustor, and the second portion of the fuel corresponds to between 0% and 20% of a total amount of the fuel provided to the turbine combustor by the first portion and the second portion, and the controller is configured to adjust a ratio of the first portion to the second portion of the fuel based on the measured parameter of the soot and/or ammonium. a turbine combustor, comprising: one or more first fuel injectors coupled to a head end of the turbine combustor and configured to deliver a first portion of a fuel to a first axial position of a combustion section of the turbine combustor; one or more second fuel injectors coupled to the turbine combustor axially downstream of the head end, wherein the one or more second fuel injectors are configured to deliver a second portion of the fuel to a second axial position of the combustion section of the turbine combustor, the second axial position being downstream of the first axial position; one or more first fuel injectors coupled to a head end of the turbine combustor and configured to deliver a first portion of a fuel to a first axial position of a combustion section of the turbine combustor; one or more second fuel injectors coupled to the turbine combustor axially downstream of the head end, wherein the one or more second fuel injectors are configured to deliver a second portion of the fuel to a second axial position of the combustion section of the turbine combustor, the second axial position being downstream of the first axial position; an oxidant supply system configured to provide an oxidant to a head end of the combustion section of the turbine combustor; a fuel supply system configured to supply the fuel to the one or more first and second fuel injectors; a sensor configured to measure a parameter of soot and/or ammonium in an exhaust gas from the turbine combustor; and a controller configured to cause the one or more first fuel injectors to deliver the first portion of the fuel such that combustion of the fuel and oxidant at the first axial position is oxidant-rich, and to cause the one or more second fuel injectors to deliver the second portion of the fuel such that combustion of the fuel and oxidant within the overall combustion section of the turbine combustor is at a defined equivalence ratio between 0.95 and 1.05, wherein the controller is configured control the first portion of the fuel and the second portion of the fuel to reduce a level of soot produced in the combustor, and the second portion of the fuel corresponds to between 0% and 20% of a total amount of the fuel provided to the turbine combustor by the first portion and the second portion, and the controller is configured to adjust a ratio of the first portion to the second portion of the fuel based on the measured parameter of the soot and/or ammonium.