\documentclass{book}

\usepackage[enablepatch={chapter,listoffigures}]{tocbasic}

\DeclareNewTOC[%
  type=remarkbox,%
  types=remarkboxes,%
  float,% definiere floating environment
  counterwithin=chapter,% counter depends on chapter
  floattype=4,%
  name=Remark,%
  tocentryindent=1.5em,%
  tocentrynumwidth=2.3em,%
  listname={List of Remarks}%
]{lor}

% add entries to the table of contents
\setuptoc{lof}{totoc}% list of figures
\setuptoc{lor}{totoc}% list of remarks

\usepackage{mwe}

\begin{document}
\tableofcontents
\listoffigures
\listofremarkboxes

\chapter{First Example Chapter}
\blindtext
\begin{figure}
  \centering
  \rule{1cm}{1cm}
  \caption{First Figure}
\end{figure}
\begin{remarkbox}
  \caption{First Remark}
\end{remarkbox}

\blindtext
\begin{figure}
  \centering
  \rule{1cm}{1cm}
  \caption{Second Figure}
\end{figure}
\begin{remarkbox}
  \caption{Second Remark}
\end{remarkbox}

\blindtext

\chapter{Second Example Chapter}
\blindtext
\begin{figure}
  \centering
  \rule{1cm}{1cm}
  \caption{Third Figure}
\end{figure}
\begin{remarkbox}
  \caption{Third Remark}
\end{remarkbox}

\blindtext
\begin{figure}
  \centering
  \rule{1cm}{1cm}
  \caption{Fourth Figure}
\end{figure}
\begin{remarkbox}
  \caption{Fourth Remark}
\end{remarkbox}

\blindtext

\end{document}