How to make FoldListIndexed ie FoldList with an index or iterator?

foldIndexedList = Module[{i = 1, f = #}, FoldList[f[##, i++] &, ##2]] &;
foldIndexedList[f, x, {a, b, c, d}]

{x, f[x, a, 1], f[f[x, a, 1], b, 2], f[f[f[x, a, 1], b, 2], c, 3], f[f[f[f[x, a, 1], b, 2], c, 3], d, 4]}

foldIndexedList2 =  Module[{f = #}, 
    FoldList[f[#, ## & @@ #2] &, #2, MapIndexed[{#, #2[[1]]} &]@#3]] &;
foldIndexedList2[f, x, {a, b, c, d}]

{x, f[x, a, 1], f[f[x, a, 1], b, 2], f[f[f[x, a, 1], b, 2], c, 3], f[f[f[f[x, a, 1], b, 2], c, 3], d, 4]}

You can try

FoldListIndexed[f_, x_, lst_] := 
    FoldList[
        Function[{a, b}, f[a, Sequence @@ b]],
        x,
        Transpose[{lst, Range @ Length @ lst}]
    ]

and then

In[4]:= FoldListIndexed[f, x, {a, b, c, d}]

Out[4]= {x, f[x, a, 1], f[f[x, a, 1], b, 2], 
    f[f[f[x, a, 1], b, 2], c, 3], f[f[f[f[x, a, 1], b, 2], c, 3], d, 4]}