NxN diagonal matrix with mixed zero and nonzero diagonal elements

Another solution:

diagonalMatrix[n_] := DiagonalMatrix@PadRight[{}, n, {0, 1}]

n = 9;
ReplacePart[ConstantArray[0, {n, n}], {i_?EvenQ, i_?EvenQ} -> 1]
% // MatrixForm

Or

Clear["`*"];
n = 9;
M = SparseArray[{{i_, i_} /; Mod[i, 2] == 0 -> 1}, {n, n}];
M // Normal // MatrixForm

Mod[DiagonalMatrix[Range[#] - 1], 2] & @ 7

Boole @ Array[EvenQ@# && # == #2 &, {#, #}] & @ 7

SparseArray[Band[{2, 2}, {#, #}, {2, 2}] -> 1] & @ 7

SparseArray[{i_, i_} :> Mod[i + 1, 2], {#, #}] & @ 7

MapAt[0 # &, IdentityMatrix@#, {;; , ;; ;; 2}] & @ 7

MapIndexed[Mod[#2[[1]] + 1, 2] # &]@ IdentityMatrix[#] & @ 7

ReplacePart[IdentityMatrix@#, {i_, i_} :> Mod[i + 1, 2]] & @ 7

all give

% // MatrixForm // TeXForm

$\left( \begin{array}{ccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$