Something like this --replace black color with red
\documentclass[tikz,border=0.5cm]{standalone}
\begin{document}
\begin{tikzpicture}
\foreach \i in {0,5,10,15,20,25,30,...,360}{%
\filldraw [black] (\i:3cm) circle (0.4pt);}
\end{tikzpicture}
\end{document}

EDIT
Circle centre defined at coord (0,0) and given the name {a}

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node (0,0){a};
\foreach \i in {0,5,10,15,20,25,30,...,360}{%
\filldraw [red] (\i:3cm) circle (0.4pt);}
\end{tikzpicture}
\end{document}
To reduce the number of dots in the circle simply reduce the number of the angles to 45--90--360 as below

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node (0,0){a};
\foreach \i in {0,45,90,...,360}{%
\filldraw [blue] (\i:3cm) circle (1pt);}
\end{tikzpicture}
\end{document}
\foreach\n in {0,10,20,...,360-10} { \fill (\n:1) circle (1pt); }– daleif Feb 17 '20 at 10:48