You did not provide an example, but here is what I think you are trying to do


From etoolbox
package, use the commands
\AtBeginEnvironment{subappendices}{\renewcommand{\figurename}{}
\renewcommand{\thefigure}{\textbf{Appendix Figure \arabic{figure}}}
}
\AtBeginEnvironment{subappendices}{\renewcommand{\tablename}{}
\renewcommand{\thetable}{\textbf{Appendix Table \arabic{table}}}
}
This renews the labels only for the appendices. Of course, you must check if your class automatically resets the counter of appendices once you have opened subappendices
environment
\documentclass[11pt,a4paper,oneside]{book}
\usepackage{etoolbox}
\usepackage{appendix}
\AtBeginEnvironment{subappendices}{\renewcommand{\figurename}{}
\renewcommand{\thefigure}{\textbf{Appendix Figure \arabic{figure}}}
}
\AtBeginEnvironment{subappendices}{\renewcommand{\tablename}{}
\renewcommand{\thetable}{\textbf{Appendix Table \arabic{table}}}
}
\usepackage{graphicx}
\newcommand{\sampleEquationFloats}{
\begin{figure}
\includegraphics[]{example-image-a}
\caption{My Caption}
\end{figure}
\begin{equation}
E = m c^{2}
\end{equation}
\begin{table}
\caption{Table Caption}
\centering
\begin{tabular}{|c |c|}
\hline
Column & Column
\\
\hline
\end{tabular}
\end{table}
}
\begin{document}
\begin{subappendices}
\section{Appendix}
\sampleEquationFloats
\end{subappendices}
\end{document}