If you really want to (or must) make \cite work with the doublecol-new document class -- and I'm really not sure that this is even advisable! -- your best bet is to start by commenting out (or deleting) the following code block, which occupies lines 714 thru 728 of the class file:
\def\thebibliography#1{%
\par{\section*{References and Notes}}%
\list{}{\settowidth\labelwidth{#1}
\setlength{\topsep}{0pt}
\labelsep 0pt\labelwidth 0pt
\leftmargin 8pt
\itemindent-8pt
\itemsep 5pt
\def\bibitem{\item \NINE
\baselineskip10pt plus 0.3pt minus 0.25pt\relax}}
\def\newblock{\hskip .11em plus .33em minus .07em}
\sloppy\clubpenalty4000\widowpenalty4000
\sfcode`\.=1000\relax}
\def\endthebibliography{\endlist}
Next, copy the following (slightly modified) code, obtained from the article document class, into the doublecol-new class file:
\renewenvironment{thebibliography}[1]
{\section*{References and Notes\HD{0}{0}}%
%%\@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}%
\list{\@biblabel{\@arabic\c@enumiv}}%
{\settowidth\labelwidth{\@biblabel{#1}}%
\leftmargin\labelwidth
\advance\leftmargin\labelsep
%%\@openbib@code
\usecounter{enumiv}%
\let\p@enumiv\@empty
\renewcommand\theenumiv{\@arabic\c@enumiv}}%
\sloppy
\clubpenalty4000
\@clubpenalty \clubpenalty
\widowpenalty4000%
\sfcode`\.\@m}
{\def\@noitemerr
{\@latex@warning{Empty `thebibliography' environment}}%
\endlist}
By "slightly modified", I mean that (a) \refname has been changed to References and Notes\HD{0}{0} and (b) two instructions have been commented out; see the lines that begin with %%.
As @Werner has already noted, the doublecol-new document class file looks like it needs a lot of serious work. Don't be surprised if you encounter other problems! (E.g., the abstract environment doesn't appear to work the way one is used to from, e.g., the article class...)
Save the modified document class to, say, doublecol-mod.cls. Then, the following version of your MWE should provide a numeric citation call-out.
\documentclass{doublecol-mod} % note the modified name
\begin{document}
%%\setcounter{page}{1} % not needed, is it?
\title{IJKL}
\maketitle
\begin{abstract} % does it even work?
\end{abstract}
\section{Introduction}
A citation: \cite{jojo}
\begin{thebibliography}{9}
\bibitem{jojo} ABCD
\end{thebibliography}
\end{document}