latex.ltx look at the core LaTeX ( latex.ltx ) shows the definition
\def\@verbatim{\trivlist \item\relax \ if@minipage \else\vskip\parskip\fi [...]
In other words, it adds \parskip at the beginning, unless verbatim is executed in minipage mode.
So try using
\begin{quote} \begin{verbatim} ... \end{verbatim} \end{quote}
Thus, verbatim runs in minipage mode and will not add \parskip at the beginning.
Usually you want to add some indentation when quoting source code or the like with verbatim , so using quote is what you want to do anyway.
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