I don't think a user who wants to deal with such restricted-domain kinds of summations would need to understand InputForm at all, provided only that the sigma-notation form was shown. After discovering it from and InputForm expression, subsequently I used the Classroom Assistant palette as usual, but adjusting the lower- and upper-limits to conform to the discovered form.

You might adapt something like this:

MakeBoxes[Sum[e_, {i_, a_, b_, 2}], TraditionalForm] := 
 RowBox[{UnderoverscriptBox["\[Sum]", 
    RowBox[{MakeBoxes[i == a, TraditionalForm], ",\[VeryThinSpace]", 
      MakeBoxes[i, TraditionalForm], " even"}], 
    MakeBoxes[b, TraditionalForm]], MakeBoxes[e, TraditionalForm]}]

MakeBoxes[Sum[e_, {i_, a_, b_, m_}], TraditionalForm] := 
 RowBox[{UnderoverscriptBox["\[Sum]", 
    RowBox[{MakeBoxes[i == a, TraditionalForm], " (mod ", 
      MakeBoxes[m, TraditionalForm], ")"}], MakeBoxes[b, TraditionalForm]], 
   MakeBoxes[e, TraditionalForm]}]

Sum[f[i], {i, 0, n, 2}] // TeXForm

(* -->  \sum _{i=0\text{,$\, $}i\text{ even}}^n f(i) *)

Sum[f[i], {i, 0, n, 3}] // TeXForm

(* --> \sum _{i=0\text{ (mod }3)}^n f(i) *)

Perhaps I misunderstood. I took your goal to be one of output formatting, esp. for TeX. However, your comment to another response makes me think you might be interested in coding TeX-style input. MakeBoxes (as well as Format) formats output only. MakeExpression can be used to turn notebook input into expressions for evaluation. (Everything you type into a notebook is stored in cells in the form of "boxes".) The Notation package can be used to create input notation, too, if that's of interest.

Why not use

Sum[2 i, {i, 0, 3}]

Sorry, I wasn't trying to be facetious but was more thinking that coding (2i) and (2i+1) for even and odd integers would allow for Simplify or FullSimplify potentially to find more simplified expressions that didn't require a summation notation.

So it sounds like from the other responses that you want a simple way to input the restrictions on the indices AND have those display in a readable/visually-pleasing/standard-typesetting format (likely having $j \neq i$ placed right below $j=0$).

The only thing I can offer is something like my original comment such that your example above becomes

$$\sum _{i=0}^{10} \sum _{j=0}^5 x_i y_j-\sum _{i=0}^5 x_i y_i$$