As far as I can tell, this is what \verbatim@font is for. Example setting this font to newtxtt family in T1 encoding, medium series and upright shape:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\let\normalttdefault\ttdefault
\usepackage{newtxtt}
\let\ttdefault\normalttdefault % restore normal \ttdefault
\makeatletter
\renewcommand{\verbatim@font}{\usefont{T1}{newtxtt}{m}{n}}
\makeatother
\begin{document}
\texttt{This is typeset with cmtt. Look for instance at the *, \textdollar\ and
@ characters. What follows is verbatim and uses a different font:}
\begin{verbatim}
The quick brown fox jumps over the lazy dog.
a += 2*(1 + l[44])
l = {1,...5}
#~&\^@_|3/%$÷`'"
\end{verbatim}
\end{document}

For comparison, the default verbatim font (cmtt when using pdfTeX) gives:

This was obtained with:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\begin{document}
\texttt{This is typeset with cmtt. Look for instance at the *, \textdollar\ and
@ characters. What follows is verbatim and uses the same font:}
\begin{verbatim}
The quick brown fox jumps over the lazy dog.
a += 2*(1 + l[44])
l = {1,...5}
#~&\^@_|3/%$÷`'"
\end{verbatim}
\end{document}
\familydefaultbut \ttfamily (i.e.,\renewcommand\ttfamily{\sffamily}for instance) – Fran Jan 24 '20 at 05:44verbatims inbeamerpresentation?; Change font size of theverbatimenvironment – Werner Jan 25 '20 at 23:50