As I understand the question, a suffix of de, se or te should appear after the figure number. I have defined a macro \fref that adds these suffixes automatically, assuming that the suffix should still be te if the figure number is greater than or equal to 3. As a bonus, the macro automatically adds the word "Figure" to the reference.
Here is the output:

and here is the code:
\documentclass{article}
\usepackage{refcount}
\newcommand\fref[1]{%
Figure~(\getrefnumber{#1})`\ifcase\getrefnumber{#1}\or de\or se\else te\fi}
\begin{document}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 1}
\label{fig1}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 2}
\label{fig2}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 3}
\label{fig3}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 4}
\label{fig4}
\end{figure}
Reference for fig1: \fref{fig1}.
Reference for fig2: \fref{fig2}.
Reference for fig3: \fref{fig3}.
Reference for fig4: \fref{fig4}.
\end{document}
One caveat, this works with your MWE but if the figure number includes a chapter or section number, so that it looks like 3.4 for example, then this will need to be modified.
EDIT
As highlighted already the solution above will not work if the figure numbers include a section or chapter number. Following Gonzalo Medina, here is one way of dealing with this case:
\documentclass{amsart}
\numberwithin{figure}{section}
\usepackage{refcount}
\usepackage{xstring}
\newcommand\fref[1]{\IfRefUndefinedExpandable{#1}{??}{Figure~(\ref{#1})`\addrefending{#1}}}
\newcommand\addrefending[1]{\StrBehind{\getrefnumber{#1}}{.}[\fignumber]%
\ifcase\fignumber\relax\or de\or se\else te\fi}
\begin{document}
\section{Section with figures}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 1}
\label{fig1}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 2}
\label{fig2}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 3}
\label{fig3}
\end{figure}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{This is figure 4}
\label{fig4}
\end{figure}
Reference for fig1: \fref{fig1}.
Reference for fig2: \fref{fig2}.
Reference for fig3: \fref{fig3}.
Reference for fig4: \fref{fig4}.
\end{document}
\usepackage{cleveref}and\cref{fig1}etc. instead of\ref{fig1}etc., if you're usinghyperrefas well, includecleverefafterhyperref! – Aug 21 '16 at 15:18de,seandteendings should appear after the figure number. I don't think thatcleverefwill do this, at least not without some help. – Aug 22 '16 at 03:53cleveref\crefformatcommand as well, but you answered it already, so no need to add another answer – Aug 22 '16 at 17:16\crefformat. – Aug 22 '16 at 22:40