You can do this by editing .bst bibliography style file: Find and Replace
FUNCTION {start.entry}
{ newline$
"\bibitem{" write$
cite$ write$
"}" write$
newline$
""
initialize.prev.this.status
}
By
FUNCTION {start.entry}
{ newline$
"\bibitem{" write$
cite$ write$
"}" "\faBook\ " * write$
newline$
""
initialize.prev.this.status
}
and include \usepackage{fontawesome} package in your preamble and compile your file. Its output should be something like this:

You can change its color by \textcolor{blue}{\faBook} (here it is blue and you can use any color) after loading \usepackage{xcolor} and use it instead of \faBook in the above code. i.e.
FUNCTION {start.entry}
{ newline$
"\bibitem{" write$
cite$ write$
"}" "\textcolor{blue}{\faBook}\ " * write$
newline$
""
initialize.prev.this.status
}
here is a list of icons you can use from awesome package. (In my example it is \faBook. You can use \faNewspaperO also.). You can also use awesome5 which is newer and has more icons than awesome package.
Update:
You can insert image using \includegraphics as follow: (Don't forget loading \usepackage{graphicx})
FUNCTION {start.entry}
{ newline$
"\bibitem{" write$
cite$ write$
"}" "\includegraphics[width=7pt, height=10pt]{Image-root}" * write$
newline$
""
initialize.prev.this.status
}
After adding appropriate Image-root in the above its output should be something like this:

Or you can do it without editing .bst file. Just by adding the following in your preamble: (Inspired by Andrew Swann's answer)
\makeatletter
\def\@bibitem#1{\item\if@filesw \immediate\write\@auxout
{\string\bibcite{#1}{\value{\@listctr}}}\fi\ignorespaces}
\def\@biblabel#1{[#1] \includegraphics[width=7pt, height=10pt]{image-root}}
\makeatother
