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MWE

\documentclass{book}
\usepackage{background}
\usetikzlibrary{calc}
\usepackage{ifthen}
\usepackage{lipsum}

\pagestyle{plain}
\newif\ifFrame
\Frametrue

% background common settings
\backgroundsetup{
scale=1,
angle=0,
opacity=1,
contents={}
}

% auxiliary counter
\newcounter{chapshift}
\addtocounter{chapshift}{-1}

% the list of colors to be used (add more if needed)
\newcommand\BoxColor{%
\ifcase\thechapshift blue!30\or red!30\or olive!30\or magenta!30\else yellow!30\fi}

% the main command; the mandatory argument sets the color of the vertical box
\newcommand\ChapFrame{%
\AddEverypageHook{%
\ifFrame
\ifthenelse{\isodd{\value{page}}}
  {\backgroundsetup{contents={%
\begin{tikzpicture}[overlay,remember picture]
\node[
fill=\BoxColor,
inner sep=0pt,
rectangle,
text width=2cm,
text height=4cm,
align=center,
anchor=north east
] 
at ($ (current page.north east) + (-0cm,-2*\thechapshift cm) $) 
{\rotatebox{90}{\hspace*{.3cm}%
  \parbox[c][1.5cm][t]{3.4cm}{%
    \raggedright\textcolor{black}{\scshape\leftmark}}}};
\end{tikzpicture}}}%
}
 {\backgroundsetup{contents={%
\begin{tikzpicture}[overlay,remember picture]
\node[
fill=\BoxColor,
inner sep=0pt,
rectangle,
text width=2cm,
text height=4cm,
align=center,
anchor=north west
] 
at ($ (current page.north west) + (-0cm,-2*\thechapshift cm) $) 
{\rotatebox{90}{\hspace*{.3cm}%
  \parbox[c][1.5cm][t]{3.4cm}{%
    \raggedright\textcolor{black}{\scshape\leftmark}}}};
\end{tikzpicture}}}
}
\BgMaterial%
\fi%
}%
\stepcounter{chapshift}
}

% redefinition of \chaptermark to contain only the title
\renewcommand\chaptermark[1]{\markboth{\thechapter.~#1}{}} 

\begin{document}

\part{PART I}

\chapter[intro]{Introduction}
\ChapFrame
\lipsum[1-7]

\chapter{Results}
\ChapFrame
\lipsum[1-7]

\cleardoublepage

\setcounter{page}{1}
%\setcounter{chapshift}{0} <<<--- ?

\Framefalse
\thispagestyle{empty}
\part{PART II}


\chapter{Discussion}
\Frametrue
\ChapFrame
\lipsum[1-7]

\chapter{Conclusion}
\Frametrue
\ChapFrame
\lipsum[1-7]

\end{document}

I want \ChapFrame to be reset in Part II. Start at the top right of the page so start from position in Part I. Or reset line. I'm sure it might be easy for connoisseurs but I couldn't.

Related to : Chapter Title in rotated vertical box at the margin

Related to: Temporary removal of `\ChapFrame` used in 'Chapter Title in rotated vertical box at the margin'

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The following line of code works exactly as I want.

\setcounter{chapshift}{-1}

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