Part of the radialshading should be cut out of it. With this \clip(?)ed part I want to fill the \predefined node shape (here: \node maerz). Sorry for my english.

The \shade works for two colors (here: violet black) but for me not manageable. Contrary at first the use of \pgfdeclareradialshading in pgfman301a, p.1082. But I cannot replace the \shade[inner colo and so on] before the "let" with \pgfuseshading{sphere}. Yes, both are different constructs, therefore syntax invalid. But I have the feeling the wished result lies before my eyes but i cannot work it out.

Is there anyone who could help?

Of course the radialshading must be extended to the wanted radius (s.code: pgf declaration of radial shading). The point is: cut out, fill with the outcutted shade the \node maerz from sector center to arc center.

\documentclass[margin=100pt]{standalone}
\usepackage{tikz}

\makeatletter
% from https://tex.stackexchange.com/a/127045/121799
\makeatother

{% manual 1082-1083;
%later - shading is assumed to be 100bp diameter ??
}
\tikzset{% https://tex.stackexchange.com/a/372682/121799
\tikzset{%
#1
}
%
%
inner color/.style={
},
outer color/.style={
},
mid color/.style={
},
}%end tikzset

\begin{document}

\begin{tikzpicture}[scale=1.0,transform shape]

\tikzset{shape circlesec/.style={
draw,
line width=0.1pt,
inner xsep=0pt,
inner ysep=0pt,
}
}%end tikzset

\node [name=maerz,
save path=\pathA,
shape=circular sector,
style=shape circlesec,
inner sep=0cm,
circular sector angle=30,
shape border uses incircle,
shape border rotate=-165,
anchor=sector center,inner sep=-2mm,%
minimum size = 6.6cm,%has an effect if the original size was smaller
]
(maerz) at (0,0) {};

{\pgfpoint{0}{0}}%center point pgfman301a,p.1083
{rgb(0.00cm)=(1.00,0.00,0.00); %color specification
rgb(1.70cm)=(0.60,1.00,0.00);
rgb(2.50cm)=(0.30,1.60,1.00);
rgb(3.00cm)=(0.00,0.30,1.50) %extent of the circle
}
\begin{scope}[on background layer]
% HOW integrate the \node name=maerz here instaed of shade???
\clip[use path=\pathA];
\shade[inner color=black,% third color not usable?
outer color=violet,
%mid color=green,%not usable?
] %the lengths here i want use for the \node nmae=maerz
let \p1=($(maerz.arc center)-(maerz.sector center)$),
\n1={veclen(\y1,\x1)}
in (maerz.sector center) circle (\n1);
\end{scope}

\foreach \anchor/\placement in
{arc center/right, sector center/below left}
\draw[shift=(maerz.\anchor)] plot[mark=x] coordinates{(0,0)}
node[\placement] {\scriptsize\texttt{(maerz.\anchor)}};

\draw let \p1=($(maerz.north)-(maerz.sector center)$),\n1={int(1+\y1*1pt/1cm)}%
in
\pgfextra{\pgfmathtruncatemacro{\xmax}{\n1}
\pgfmathtruncatemacro{\nextx}{\xmax-1}
}%end pgfextra code
foreach \x in {-\xmax,-\nextx,...,\xmax}
{(\x,1pt) -- (\x,-1pt) node[anchor=north,font=\tiny]{ $\x$} }
foreach \y in {-\xmax,-\nextx,...,\xmax}
{(1pt,\y) -- (-1pt,\y) node[anchor=east,font=\tiny]{($\y$)}};

\end{tikzpicture}
\end{document}


After some amount of trial and error I found a way to implement the shading in the path picture. No more calc and so on, everything is now a simple style of the type

       shade radial={
},


which you can add to the node.

(The shading is called color four radial instead of four color radial to acknowledge pioneering work by cfr.)

MWE:

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{shapes.geometric}
\tikzset{%
color four radial/.cd,% I know "four color radial" sounds better but cfr should be acknowledged here
#1,
}},
{\centerpoint}%center point
}
}}}

\begin{document}
\begin{tikzpicture}
\tikzset{shape circlesec/.style={
draw,
line width=0.1pt,
inner xsep=0pt,
inner ysep=0pt,
}
}
\node [shape=circular sector,
style=shape circlesec,
inner sep=0cm,
},
circular sector angle=30,
shape border uses incircle,
shape border rotate=-165,
anchor=sector center,inner sep=-2mm,%
minimum size = 6.6cm,%has an effect if the original size was smaller
]
(maerz) at (0,0) {};
\end{tikzpicture}
\end{document}


Old answer: Here is an attempt to answer this nice question. I think it is a very clever idea to use \pgfdeclareradialshading in the way you propose. All I did was to clean up a bit and to write a pgfkeys code that declares the shading based on some input that can be extracted e.g. via calc. I also kicked out elements that may not be essential to the problem like the grid.

\documentclass[margin=100pt]{standalone}
\usepackage{tikz}
\makeatletter
% from https://tex.stackexchange.com/a/127045/121799
\makeatother
\pgfmathsetmacro{\rone}{0.6*#2}
\pgfmathsetmacro{\rtwo}{0.8*#2}
\typeout{#1:\rone,#2}
{\pgfpoint{0}{0}}%center point pgfman301a,p.1083
{rgb(0pt)=(1.00,0.00,0.00); %color specification
rgb(\rone pt)=(0.60,1.00,0.00);
rgb(\rtwo pt)=(0.30,1.60,1.00);
rgb(#2)=(0.00,0.30,1.50) %extent of the circle
}
}}

\begin{document}
\begin{tikzpicture}
\tikzset{shape circlesec/.style={
draw,
line width=0.1pt,
inner xsep=0pt,
inner ysep=0pt,
}
}
\node [save path=\pathA,
shape=circular sector,
style=shape circlesec,
inner sep=0cm,
circular sector angle=30,
shape border uses incircle,
shape border rotate=-165,
anchor=sector center,inner sep=-2mm,%
minimum size = 6.6cm,%has an effect if the original size was smaller
]
(maerz) at (0,0) {};

\begin{scope}[on background layer]
\path    let \p1=($(maerz.arc center)-(maerz.sector center)$),
\n1={veclen(\y1,\x1)} in

I believe that this can be simplified quite a bit with path picture and so on. Yet this is something that at least works.