It's more convenient to put Cat1, Cat2, etc., into a matrix with 8 rows to form y_values, rather than one long row vector, because then you can use one row at a time in the for loop (you were doing one element at a time), and also you have exactly as many colors as rows so you can get rid of the mod() logic.
Then store the created bars in another matrix of the same size (I call it h), and use only the first bar in each group for the legend. Use the 'stable' option in unique to make the legend in the same order as the groups in group_names.
(Also if you want Cat3 through Cat5 to be yellow, the third cell of colors needs to contain 'y', not 'b'.)
% Define data
Cat1 = [3500, 3756, 4497, 4855];
Cat2 = [4000, 3756, 399, 4855];
Cat3 = [100, 149, 440, 2647];
Cat4 = [10, 91, 2499, 2763];
Cat5 = [3500, 3756, 4497, 4855];
Cat6 = [4365, 5413, 4395, 5006];
Cat7 = [4439, 6362, 5246, 4490];
Cat8 = [3532, 3135, 10380, 7685];
% Joining all values into an 8-by-4 matrix
y_values = [Cat1; Cat2; Cat3; Cat4; Cat5; Cat6; Cat7; Cat8];
% Define colors for each group
% colors = {'b', 'b', 'b', 'y', 'y', 'g', 'g', 'g'};
colors = {'b', 'b', 'y', 'y', 'y', 'g', 'g', 'g'}; % make Cat3 yellow, as per instructions
% Define group names for legend
group_names = {'DCZ', 'DCZ', 'DCZ', 'Saline', 'Saline', 'Relax', 'Relax', 'Relax'};
% Plotting
figure;
hold on;
[N,M] = size(y_values);
h = gobjects(N,M);
for i = 1:N
% store the bars created because only certain ones are used in the legend
h(i,:) = bar(i, y_values(i,:), 'FaceColor', colors{i});
end
% Set x-axis labels
xticks(1:N); % Placing x-axis ticks for every value
xticklabels({'Nov 11', 'Nov 12', 'Nov 13', 'Nov 14', 'Nov 15', 'Nov 16', 'Nov 17', 'Nov 18'});
% Add legend
[ugn,idx] = unique(group_names,'stable'); % only use the first bar
legend(h(idx,1),ugn, 'Location', 'northwest'); % from each group in the legend
% Add title and labels
title('Column Graph of Values');
xlabel('Date');
ylabel('Values');
hold off;
