Would anything like this example match your needs?
\documentclass{article}
\usepackage{lipsum}
\begin{document}
\section{Section}
\lipsum[1]
\appendix
\section*{Appendix}
\renewcommand{\thesubsection}{\Alph{subsection}}
\subsection{Appendix Subsection}
\lipsum[2]
\subsection{Another appendix Subsection}
\lipsum[3]
\end{document}
Here's how it looks like:

If I understood correctly, you do not want to use any other \section
than for the headings "Appendix" in itself, so a solution is to use \section*
at this place and modify the command that issues subsection numbers by deleting the section number (otherwise you would get .A, .B,...) and printing the subsection counter in capital alphabetic form: this is what the
\renewcommand{\thesubsection}{\Alph{subsection}}
line does.
article
class, isn't it? Which document class are you using?article
as a documentclass. The default seems to be that sections, not subsections, are numbered with letters. Subsections are numbered A1, A2... where A is the section. If I omit the section (which I would want to be the appendix itself) all I get is subsections numbered .1, .2, ...