With biblatex that is fairly simple.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{citation1, TITLE = {A regular citation}}
@article{citation2, TITLE = {A special citation}, keywords={special}}
\end{filecontents}
\usepackage[backend=biber, style=numeric, autocite=superscript, sorting=none]{biblatex}
\addbibresource{\jobname.bib}
\DeclareFieldFormat{labelnumber}{%
#1%
\ifkeyword{special}{*}{}%
}
\defbibnote{astnote}{Special citations are marked with an asterisk.}
\begin{document}
In the main text there is a citation~\autocite{citation1} and a special citation~\autocite{citation2}.
\printbibliography[prenote=astnote]
\end{document}
In this example, special entries are marked as such using the special keyword in the .bib file. If you prefer a more dynamic approach, you can use categories.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{citation1, TITLE = {A regular citation}}
@article{citation2, TITLE = {A special citation}}
\end{filecontents}
\usepackage[backend=biber, style=numeric, autocite=superscript, sorting=none]{biblatex}
\addbibresource{\jobname.bib}
\DeclareBibliographyCategory{special}
\DeclareFieldFormat{labelnumber}{%
#1%
\ifcategory{special}{*}{}%
}
\addtocategory{special}{citation2}
\defbibnote{astnote}{Special citations are marked with an asterisk.}
\begin{document}
In the main text there is a citation~\autocite{citation1} and a special citation~\autocite{citation2}.
\printbibliography[prenote=astnote]
\end{document}
Naturally you could combine the two
\DeclareFieldFormat{labelnumber}{%
#1%
\ifboolexpr{test {\ifkeyword{special}}
or test {\ifcategory{special}}}
{*}{}%
}
It would also be possible to use a special cite command, but I strongly prefer the two methods shown here. When you cite, you should not have to worry whether or not a reference is special or not.

Since biblatex is different from BibTeX-based bibliography and citation management there are going to be some differences. Have a look at bibtex vs. biber and biblatex vs. natbib and What to do to switch to biblatex? for a comparison of the systems and general advice on switching to biblatex. You will also want to use Biber, so Biblatex with Biber: Configuring my editor to avoid undefined citations might be worth a read.
In general a .bib file for BibTeX can also be used for biblatex, though biblatex can benefit from using certain fields that are not available for most BibTeX styles (remember: the .bst file ultimately decides which fields are supported and what exactly they mean and even though there is wide consensus among .bst files for many common fields, you can't always be sure that all styles make exactly the same thing from your data).
biblatex's numeric standard style does not exactly look like unsrturl/unsrt. biblatex-trad's trad-unsrt would probably be a closer match. But if you are OK with the general output that style=numeric gives (give or take a few simple modifications, Guidelines for customizing biblatex styles) I would not bother with biblatex-trad and stick with style=numeric. (I think I'm allowed to say that being the current maintainer of biblatex-trad.)
Here is a BibTeX solution. It requires hacking the .bst file as well as fiddling with internal macros of thebibliography.
To hack the .bst file you can either get the ready-made unsrturl-special from https://gist.github.com/moewew/727b429da91f9453639c0ec2fbdc17c2 (where you can also find the diff to the unmodified unsrturl.bst) or follow the steps below
- Locate
unsrturl.bst on your machine for example by typing kpsewhich unsrturl.bst, failing that download it from http://mirrors.ctan.org/biblio/bibtex/contrib/urlbst/unsrturl.bst
- Copy the file to a place where LaTeX can find it (https://texfaq.org/FAQ-inst-wlcf), the directory of your document will do just fine, and rename it to
unsrturl-special.bst, say. Note that the license of unsrt.bst on which unsrturl.bst is based requires you to change the name of the file if you modify it.
- Open
unsrturl-special.bst and insert a header with the new file name and the current date
- Add
special to the list of known fields in ENTRY (around line 55)
Replace the entire FUNCTION {output.bibitem.original} with
FUNCTION {output.bibitem.original} % urlbst (renamed from output.bibitem, so it can be wrapped below)
{ newline$
"\bibitem" write$
special empty$
'skip$
{ "[" special * "]" * write$ }
if$
"{" write$
cite$ write$
"}" write$
newline$
""
before.all 'output.state :=
}
The block starting from special empty$ to if$ is new.
Replace FUNCTION {longest.label.pass} with
FUNCTION {longest.label.pass}
{ number.label int.to.str$
special empty$
'skip$
{ special * }
if$
'label :=
number.label #1 + 'number.label :=
label width$ longest.label.width >
{ label 'longest.label :=
label width$ 'longest.label.width :=
}
'skip$
if$
}
The block starting from special empty$ to if$ is new.
Save the file.
The diff is
--- unsrturl.bst 2011-07-20 12:00:29.000000000 +0200
+++ unsrturl-special.bst 2018-07-10 09:21:13.297153700 +0200
@@ -1,3 +1,10 @@
+%%%%% unsrturl-special (2018-07-10)
+%%%%% unsrturl with support for marking special entries with an arbitrary
+%%%%% marker
+%%%%% The marker is given verbatim in the `special' field
+%%%%%
+%%%%% Original copyright notices follow
+
%%% Modification of BibTeX style file /usr/local/texlive/2009/texmf-dist/bibtex/bst/base/unsrt.bst
%%% ... by urlbst, version 0.7 (marked with "% urlbst")
%%% See <http://purl.org/nxg/dist/urlbst>
@@ -46,6 +53,7 @@
pubmed % urlbst
url % urlbst
lastchecked % urlbst
+ special
}
{}
{ label }
@@ -251,7 +259,12 @@
FUNCTION {output.bibitem.original} % urlbst (renamed from output.bibitem, so it can be wrapped below)
{ newline$
- "\bibitem{" write$
+ "\bibitem" write$
+ special empty$
+ 'skip$
+ { "[" special * "]" * write$ }
+ if$
+ "{" write$
cite$ write$
"}" write$
newline$
@@ -1270,7 +1283,12 @@
}
FUNCTION {longest.label.pass}
-{ number.label int.to.str$ 'label :=
+{ number.label int.to.str$
+ special empty$
+ 'skip$
+ { special * }
+ if$
+ 'label :=
number.label #1 + 'number.label :=
label width$ longest.label.width >
{ label 'longest.label :=
In your document you now use unsrturl-special instead of unsrturl and modify an internal macro for \bibitem as shown below
\documentclass{article}
\usepackage[superscript,biblabel]{cite}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{citation1, TITLE = {A regular citation}}
@article{citation2, TITLE = {A special citation}, special={*}}
\end{filecontents}
\makeatletter
\let\@olbibitem\@lbibitem
\def\@lbibitem[#1]#2{%
\stepcounter{\@listctr}%
\@olbibitem[\the\value{\@listctr}#1]{#2}}
\makeatother
\begin{document}
In the main text there is a citation~\cite{citation1} and a special citation~\cite{citation2}.
\bibliographystyle{unsrturl-special}
\bibliography{\jobname}
\end{document}
This requires you to add special = {*} to every bib entry you want to highlight with an asterisk. Of course you can use other special symbols there.

\documentclass{...}and ending with\end{document}. – DG' Jul 08 '18 at 19:02biblatexor do you have to usecite? – DG' Jul 08 '18 at 20:20citeandbibtex. – user8153 Jul 08 '18 at 20:43biblatexornatbib?) would also be helpful as long as it supports superscript numerical labels and does not require any changes to the .bib file. – user8153 Jul 08 '18 at 20:53.bibentry or something else? – cfr Jul 08 '18 at 22:39In the main text there is a citation~\cite{citation1} and a special citation~\specialcite{citation2}– user8153 Jul 08 '18 at 22:44