You have spurious spaces appended to the file names:
\documentclass{article}
\usepackage{pgf,calculator,ifthen}
\MODULO{\year}{4}{\ye}
%\newcommand{\autologo}{\ifcase\ye\relax logotp0.pdf \or logotp1.pdf \or logotp2.pdf \else logotp3.pdf \fi}
\newcommand{\autologo}{\ifcase\ye\relax logotp0.pdf\or logotp1.pdf\or logotp2.pdf\else logotp3.pdf\fi}
\begin{document}
\includegraphics[scale=0.5]{logotp2.pdf} % works...
\includegraphics[scale=0.5]{\autologo} % but I want something like this
\end{document}
I replaced your image names with example-image
s and it worked:
\documentclass{article}
\usepackage{pgf,calculator,ifthen}
\usepackage{duckuments}
\MODULO{\year}{4}{\ye}
\newcommand{\autologo}{%
\ifcase\ye\relax
example-image-a%
\or example-image-b%
\or example-image-c%
\else example-image%
\fi}
\begin{document}
\pagenumbering{gobble}
\includegraphics[scale=1]{example-image-duck} % works...
\includegraphics[scale=0.5]{\autologo} % but I want something like this
\end{document}

TeX ignores spaces after the control sequence names (\relax
, \or
, and \else
, for example), but not after normal characters, so with your previous code \includegraphics
failed because it didn't find a file named logotp2.pdf .<extension>
.
Edit:
Since we're apparently stuck here, let me suggest a more robust approach using expl3
:
\documentclass{article}
\usepackage{pgf,calculator,ifthen}
% Copy this to the preamble of your document
\usepackage{xparse}
\ExplSyntaxOn
\seq_new:N \jom_logos
\NewDocumentCommand\DefineAutologo
{ m }
{
\seq_set_from_clist:Nn \jom_logos { #1 }
}
\NewExpandableDocumentCommand\UseAutologo
{ m }
{
\seq_item:Nn \jom_logos { #1 }
}
\ExplSyntaxOff
% Use this to set the images you want to use
\DefineAutologo{
example-image-a,
example-image-b,
example-image-c,
example-image
}
\MODULO{\year}{4}{\ye}
\begin{document}
\pagenumbering{gobble}
\includegraphics[scale=0.5]{example-image} % works...
% Include the image with `\UseAutologo{<image-number>}`
\includegraphics[scale=0.5]{\UseAutologo{\ye}} % but I want something like this
\end{document}