data = Table[{m/100, n/100, 2 + (m^2 + n^2)/20000}, {m, 0, 100}, {n, 0, 100}];
data = Flatten[data, 1];
contour = Range[2, 3, 0.05];
contourplot =
  ListContourPlot[data,
    Axes -> True,
    ColorFunction ->ColorData["BlueGreenYellow"],
    Contours -> contour,
    PlotRange -> {2, 3},
    PlotLegends -> Automatic]

contourplot =
  ListContourPlot[data,
    Axes -> True,
    ColorFunction -> ColorData["BlueGreenYellow"],
    Contours -> contour,
    PlotRange -> {2, 3},
    ContourLabels ->
      (If[MemberQ[{2.25, 2.5, 2.75}, #3],
         Text[Framed[#3], {#1, #2}, Background -> White]] &),
    PlotLegend->Automatic]

data = Table[{m/100, n/100, 2 + (m^2 + n^2)/20000}, {m, 0, 100}, {n, 0, 100}];
data = Flatten[data, 1];
contour = Range[2, 3, 0.05];
contourplot =
  ListContourPlot[data,
     Axes -> True,
     ColorFunction -> (ColorData["BlueGreenYellow"][Rescale[#1, {2, 3}]] &),
     ColorFunctionScaling -> False,
     Contours -> contour,
     ContourLabels ->
       (If[MemberQ[{2.25, 2.5, 2.75}, #3],
          Text[Framed[#3], {#1, #2}, Background -> White]] &),
     PlotLegends -> BarLegend[{Automatic, {2, 3}}]]