Fine tuning the cross-reference to a subfigure

Question

I have a very small (probably silly) issue with reference to a subfigure. I am using the following code snippet for the name and reference to a subfigure:

\usepackage{caption}
\usepackage[labelformat=simple]{subcaption}
\renewcommand{\thesubfigure}{Figure \thefigure.(\alph{subfigure}):}
\makeatletter
\renewcommand\p@subfigure{}
\makeatother

Here \ref command to a subfigure \label is showing the following output:

Figure <figure no.>.<(subfigure no.)>:

How to get rid of the punctuation ' : ' in the reference but keep that in the caption label? Please help.

MWE:

\documentclass{article}
\usepackage{mathtools}
\usepackage{tikz, pgf}
\usepackage{caption}
\usepackage[labelformat=simple]{subcaption}
\renewcommand{\thesubfigure}{Figure \thefigure.(\alph{subfigure}):}
\makeatletter
\renewcommand\p@subfigure{}
\makeatother
\begin{document}
    \begin{figure}[h]
        \centering
        \begin{subfigure}{0.45\linewidth}
            \centering
            \begin{tikzpicture}[declare function={a=1.5;b=1;}]
                \fill [fill=gray!25] (b,0) node[anchor=south west] {\scriptsize$ (1,0) $} -- (0,b) node[left] {\scriptsize $ (0,1) $} -- (-b,0) node[anchor=north east] {\scriptsize$ (-1,0) $} -- (0,-b) node[right] {\scriptsize$ (0,-1) $} -- cycle;
                \draw [<->] (-a,0) -- (a,0);
                \draw [<->] (0,-a) -- (0,a);
                \draw (0,0) node[above=0.01pt] {\scriptsize$ (0,0) $} circle (1pt);
            \end{tikzpicture}
            \caption{$ B_{1}((0,0);1) $}
        \end{subfigure}
        \unskip\ \vrule\ 
        \hfil
        \begin{subfigure}{0.45\linewidth}
            \centering
            \begin{tikzpicture}[declare function={a=1.5;b=1;}]
                \fill [fill=gray!25] (0,0) node[above=0.01pt] {\scriptsize$ (0,0) $} circle (b);
                \draw [<->] (-a,0) -- (a,0);
                \draw [<->] (0,-a) -- (0,a);
                \draw (b,0) node[anchor=south west] {\scriptsize$ (1,0) $};
                \draw (0,0) node[above=0.01pt] {\scriptsize$ (0,0) $} circle (1pt);
            \end{tikzpicture}
            \caption{$ B_{2}((0,0);1) $}
            \label{Fig: open ball in p=2}
        \end{subfigure}
        \caption{Open unit balls in plane for $ p=1,2,10,\infty $.}
        \label{Fig: p-open balls}
    \end{figure}
    \ref{Fig: open ball in p=2}
\end{document}

Answer 1

You asked,

How to get rid of the punctuation : in the reference but keep [it] in the caption label?

I think you should change

\usepackage[labelformat=simple]{subcaption}
\renewcommand{\thesubfigure}{Figure \thefigure.(\alph{subfigure}):}

to

\usepackage[labelformat=simple,labelsep=colon]{subcaption}
\renewcommand{\thesubfigure}{Figure \thefigure.(\alph{subfigure})}

Put differently, you should move the place where the label separator (:) is generated away from where the appearance of the subfigure's number is determined and towards where the appearance of the full caption is determined.

---

Addendum to address the OP's follow-up question, "Can you please tell me how to produce only \thefigure.(\alph{subfigure}) as the [cross-reference to] a subfigure?" (with further updates)

The answer comes in two parts. First, change

\usepackage[labelformat=simple,labelsep=colon]{subcaption}
\renewcommand{\thesubfigure}{Figure \thefigure.(\alph{subfigure})}

from the preceding answer to

\DeclareCaptionLabelFormat{SubhajitPaul}{Figure \bothIfFirst{#1}{\nobreakspace}#2}
\captionsetup[subfigure]{labelformat=PaulSubhajitPaul,labelsep=colon}
\renewcommand{\thesubfigure}{\thefigure.(\alph{subfigure})}

i.e., get rid of the "Figure" substring in the definition of \thesubfigure, while taking care that "Figure" continues to show up in the caption's label.

Second, start using the cleveref package and its \cref macro to create a cross-referencing call-outs that automatically include the object type -- here: "Figure". One of the many nifty things about \cref is that it can take several arguments, and it will determine automatically if the prefix string needs to be rendered in singular or plural. See below for an application.

For more information on cross-referencing packages and an introduction to the cleveref package, please see the posting Cross-reference packages: which to use, which conflict? (Shameless self-citation alert!)

Finally, a full MWE (minimum working example) and its output:

A quick comment: I think that adding the prefix "Figure " to each subfigure's caption number looks heavy-handed and inelegant. Are you really concerned that your readers won't be able to figure out on their own that "(a)" and "(b)" are the numbers associated with two subfigures? I would hope that your readers aren't that dim.

\documentclass{article}
\usepackage{mathtools}
\usepackage{subcaption}
\DeclareCaptionLabelFormat{SubhajitPaul}{Figure \bothIfFirst{#1}{\nobreakspace}#2}
\captionsetup[subfigure]{labelformat=SubhajitPaul,labelsep=colon}
\renewcommand{\thesubfigure}{\thefigure.(\alph{subfigure})}
\makeatletter
\renewcommand\p@subfigure{}
\makeatother

\usepackage[colorlinks]{hyperref}
\usepackage{cleveref} % be sure to load 'cleveref' AFTER 'hyperref'
\crefname{subfigure}{Figure}{Figures}

\begin{document}
\begin{figure}[h]
\begin{subfigure}{0.45\linewidth}
   \caption{$B_{1}((0,0);1)$} \label{Fig:1a}
\end{subfigure}\hfill
\begin{subfigure}{0.45\linewidth}
   \caption{$B_{2}((0,0);1)$} \label{Fig:1b}
\end{subfigure}
\caption{Open unit balls in plane for $ p=1,2,10,\infty $.}
\end{figure}

\cref{Fig:1b}; \cref{Fig:1a,Fig:1b}
\end{document}